Quiz 7 Estimation
1. Which of the following statements is not correct?
a. When an interval estimate is associated with a degree of confidence that it actually
includes the population parameter of interest, it is referred to as a confidence interval
b. If the population mean and population standard deviation are both known, one can
make probability statements about individual x values taken from the population
c. If the population mean and population standard deviation are both known, one can
use the central limit theorem and make probability statements about the means of
samples taken from the population
d. If the population mean is unknown, one can use sample data as the basis from
which to make probability statements about the true (but unknown) value of the
population mean
*e. when sample data are used for estimating a population mean, sampling error will
not be present since the observed sample statistic will not differ from the actual value
of the population parameter
2. Inferential statistics is the:
a. process of using a population parameter to estimate the values for sample statistics
*b. process of using sample statistics to estimate population parameters
c. process which allows the researcher to determine the exact values for population
parameters
d. process that eliminates the problem of sampling error
e. branch of statistics involving using population parameters to estimate sampling
distributions
3. Which of the following statements are correct?
a. a point estimate is an estimate of the range of a population parameter
b. a point estimate is an unbiased estimator if its standard deviation is the same as the
actual value of the population standard deviation
*c. a point estimate is a single value estimate of the value of a population parameter
d. all of the above statements are correct
e. none of the above statements are correct
4. A point estimator is defined as:
a. the average of the sample values
b. the average of the population values
*c. a single value that is the best estimate of an unknown population parameter
d. a single value that is the best estimate of an unknown sample statistic
e. a number which can be used to estimate a point in time which is unknown
5. Which of the following statements is/are correct?
*a. an interval estimate is an estimate of the range of possible values for a population
parameter
b. an interval estimate describes a range of values that is likely not to include the
actual population parameter
c. an interval estimate is an estimate of the range for a sample statistic
d. all of the statements above are correct
e. none of the statements above are correct
6. A confidence interval is defined as:
a. a point estimate plus or minus a specific level of confidence
*b. a lower and upper confidence limit associated with a specific level of confidence
c. an interval that has a 95% probability of containing the population parameter
d. a lower and upper confidence limit that has a 95% probability of containing the
population parameter
e. an interval used to infer something about an unknown sample statistic value
7. The term 1 – α refers to the:
a. probability that a confidence interval does not contain the population parameter
b. the level of confidence minus one
*c. the level of confidence
d. the level of confidence plus one
e. the level of significance
8. A 95% confidence interval for the population mean is calculated to be 75.29 to
81.45. If the confidence level is reduced to 90%, the confidence interval will:
*a. become narrower
b. remain the same
c. become wider
d. double in size
e. most likely no longer include the true value of the population mean
9. A 95% confidence interval for the population mean is calculated to be 75.29 to
81.45. If the confidence level is increased to 98%, the confidence interval will:
a. become narrower
b. remain the same
*c. become wider
d. double in size
e. most likely no longer include the true value of the population mean
10. In the formula for the confidence interval, zα/2 is part of the formula. What does
the subscript α/2 refer to?
a. the level of confidence
b. the level of significance
c. the probability that the confidence interval will contain the population mean
d. the probability that the confidence interval will not contain the population mean
*e. the area in the lower tail or upper tail of the sampling distribution of the sample
mean
11. Which of the statements below completes the following statement correctly? The
larger the level of confidence used in constructing a confidence interval estimate of
the population mean, the:
a. smaller the probability that the confidence interval will contain the population mean
b. the smaller the value of zα/2
c. the narrower the confidence interval
*d. the wider the confidence interval
e. the more the width of the confidence interval remains the same
12. Which one of the statements below is correct?
a. If n, the sample size, increases, the confidence interval becomes wider
*b. A 90% confidence interval for the population mean is narrower than a 95%
confidence interval for the population mean
c. As the population standard deviation increases, the confidence interval becomes
narrower
d. If α = 0.01, it implies that we are 1% confident that the population mean will lie
between the confidence limits
e. none of the above statements is correct
13. The boundaries of a confidence interval are called:
a. Confidence levels
b. The test statistics
c. The degrees of confidence
*d. The confidence limits
e. Significance levels
14. What value of z would you use to calculate the 80% confidence interval for a
population mean, given that you know the population standard deviation, the sample
size and the sample mean of your sample?
a. z = 1.96
b. z = 2.58
c. z = 0.84
*d. z = 1.28
e. z = 1.645
15. Which of the following statements is false with regards to the width of a
confidence interval?
a. The sample mean from which the interval is constructed is located half way
between the boundaries of the confidence interval
b. The width of the interval increases when the sample size is decreased
c. The width of the interval decreases when the significance level is increased
*d. The width of the interval decreases when the sample mean is decreased
e. The width of the interval increases when the confidence level is increased
16. After constructing a confidence interval estimate for a population mean, you
believe that the interval is useless because it is too wide. In order to correct this
problem, you need to:
a. Increase the population standard deviation
*b. Increase the sample size
c. Increase the level of confidence
d. Increase the sample mean
e. Decrease the sample size
17. The problem with relying on a point estimate of a population parameter is that the
point estimate
a. has no variance
b. might be unbiased
c. might not be relatively efficient
*d. does not tell us how close or far the point estimate might be from the parameter
e. may not be consistent
18. A federal auditor for nationally chartered banks from a random sample of 100
accounts found that the average demand deposit balance at the First National Bank of
a small town was R549.82. If the auditor needed a point estimate for the population
mean for all accounts at this bank, what would she use?
*a. The average of R549.82 for this sample.
b. The average of R54.98 for this sample.
c. There is no acceptable value available.
d. She would survey the total of all accounts and determine the mean.
e. The mean would be impossible to calculate without further information
19. Which one of the statements below is correct?
a. If the significance level is equal to 0.1, it implies that we are 10% confident that the
population mean will lie between the confidence limits
b. If the sample size increases the confidence interval becomes wider
c. As the population standard deviation increases, the confidence interval becomes
narrower
*d. A 90% confidence interval for the population mean is narrower than a 95%
confidence interval for the population mean
e. Increasing the significance level increases the width of the confidence interval
20. Sand is packed into bags which are then weighed on scales. It is known that if full
bags of sand are intended to weigh μ kg, then the weight recorded by the scales will
be normally distributed with a mean μ kg and a standard deviation of 0.36kg. A
particular bag of sand was weighed four times and the weight recorded each time was
different. The sample mean weight was recorded as 34.7kg. What is a 95%
confidence interval for the true weight of the full bag of sand?
*a. 34.35 to 35.05kg
b. 35.85 to 36.55kg
c. 34.21 to 35.19kg
d. 34.48 to 34.92kg
e. 37.75 to 38.45kg
21. Sand is packed into bags which are then weighed on scales. It is known that if full
bags of sand are intended to weigh μ kg, then the weight recorded by the scales will
be normally distributed with a mean μ kg and a standard deviation of 0.36kg. A
particular bag of sand was weighed four times and the weight recorded each time was
different. The sample mean weight was recorded as 36.2kg. What is a 95%
confidence interval for the true weight of the full bag of sand?
a. 34.35 to 35.05kg
*b. 35.85 to 36.55kg
c. 34.21 to 35.19kg
d. 34.48 to 34.92kg
e. 37.75 to 38.45kg
22. Sand is packed into bags which are then weighed on scales. It is known that if full
bags of sand are intended to weigh μ kg, then the weight recorded by the scales will
be normally distributed with a mean μ kg and a standard deviation of 0.5kg. A
particular bag of sand was weighed four times and the weight recorded each time was
different. The sample mean weight was recorded as 34.7kg. What is a 95%
confidence interval for the true weight of the full bag of sand?
a. 34.35 to 35.05kg
b. 35.85 to 36.55kg
*c. 34.21 to 35.19kg
d. 34.48 to 34.92kg
e. 37.75 to 38.45kg
23. Sand is packed into bags which are then weighed on scales. It is known that if full
bags of sand are intended to weigh μ kg, then the weight recorded by the scales will
be normally distributed with a mean μ kg and a standard deviation of 0.36kg. A
particular bag of sand was weighed ten times and the weight recorded each time was
different. The sample mean weight was recorded as 34.7kg. What is a 95%
confidence interval for the true weight of the full bag of sand?
a. 34.35 to 35.05kg
b. 35.85 to 36.55kg
c. 34.21 to 35.19kg
*d. 34.48 to 34.92kg
e. 37.75 to 38.45kg
24. Sand is packed into bags which are then weighed on scales. It is known that if full
bags of sand are intended to weigh μ kg, then the weight recorded by the scales will
be normally distributed with a mean μ kg and a standard deviation of 0.36kg. A
particular bag of sand was weighed four times and the weight recorded each time was
different. The sample mean weight was recorded as 38.1kg. What is a 95%
confidence interval for the true weight of the full bag of sand?
a. 34.35 to 35.05kg
b. 35.85 to 36.55kg
c. 34.21 to 35.19kg
d. 34.48 to 34.92kg
*e. 37.75 to 38.45kg
25. An analyst is conducting a hypothesis test to determine if the mean time spent on
investment research by portfolio managers is different from 3 hours per day. The test
uses a random sample of 64 portfolio managers, where the sample mean time spent on
research is found to be 2.5 hours. The population standard deviation is 1.5 hours.
What is the 99% confidence interval for the population mean time spent on
investment research by portfolio managers?
*a. (2.02, 2.98)
b. (2.22, 3.18)
c. (1.86, 3.14)
d. (2.11, 2.89)
e. (1.82, 2.78)
26. An analyst is conducting a hypothesis test to determine if the mean time spent on
investment research by portfolio managers is different from 3 hours per day. The test
uses a random sample of 64 portfolio managers, where the sample mean time spent on
research is found to be 2.7 hours. The population standard deviation is 1.5 hours.
What is the 99% confidence interval for the population mean time spent on
investment research by portfolio managers?
a. (2.02, 2.98)
*b. (2.22, 3.18)
c. (1.86, 3.14)
d. (2.11, 2.89)
e. (1.82, 2.78)
27. An analyst is conducting a hypothesis test to determine if the mean time spent on
investment research by portfolio managers is different from 3 hours per day. The test
uses a random sample of 64 portfolio managers, where the sample mean time spent on
research is found to be 2.5 hours. The population standard deviation is 2 hours. What
is the 99% confidence interval for the population mean time spent on investment
research by portfolio managers?
a. (2.02, 2.98)
b. (2.22, 3.18)
*c. (1.86, 3.14)
d. (2.11, 2.89)
e. (1.82, 2.78)
28. An analyst is conducting a hypothesis test to determine if the mean time spent on
investment research by portfolio managers is different from 3 hours per day. The test
uses a random sample of 100 portfolio managers, where the sample mean time spent
on research is found to be 2.5 hours. The population standard deviation is 1.5 hours.
What is the 99% confidence interval for the population mean time spent on
investment research by portfolio managers?
a. (2.02, 2.98)
b. (2.22, 3.18)
c. (1.86, 3.14)
*d. (2.11, 2.89)
e. (1.82, 2.78)
29. An analyst is conducting a hypothesis test to determine if the mean time spent on
investment research by portfolio managers is different from 3 hours per day. The test
uses a random sample of 64 portfolio managers, where the sample mean time spent on
research is found to be 2.3 hours. The population standard deviation is 1.5 hours.
What is the 99% confidence interval for the population mean time spent on
investment research by portfolio managers?
a. (2.02, 2.98)
b. (2.22, 3.18)
c. (1.86, 3.14)
d. (2.11, 2.89)
*e. (1.82, 2.78)
30. A researcher wants to investigate the amount of lead per litre of waste water
produced by her company. She plans to use statistical methods to estimate the
population mean of lead content per litre of water. Based on previous recordings she
assumes that the lead content is normally distributed with a standard deviation of
20mg per litre. She decides that she can afford a sample size of 500, but not larger,
and with this sample finds a sample mean of 632mg of lead per litre. The 95%
confidence interval for the mean lead content per litre of waste water produced by her
company then is:
*a. (630.25, 633.75)
b. (639.25, 642.75)
c. (629.81, 634.19)
d. (630.04, 633.96)
e. (630.69, 633.31)
31. A researcher wants to investigate the amount of lead per litre of waste water
produced by her company. She plans to use statistical methods to estimate the
population mean of lead content per litre of water. Based on previous recordings she
assumes that the lead content is normally distributed with a standard deviation of
20mg per litre. She decides that she can afford a sample size of 500, but not larger,
and with this sample finds a sample mean of 641mg of lead per litre. The 95%
confidence interval for the mean lead content per litre of waste water produced by her
company then is:
a. (630.25, 633.75)
*b. (639.25, 642.75)
c. (629.81, 634.19)
d. (630.04, 633.96)
e. (630.69, 633.31)
32. A researcher wants to investigate the amount of lead per litre of waste water
produced by her company. She plans to use statistical methods to estimate the
population mean of lead content per litre of water. Based on previous recordings she
assumes that the lead content is normally distributed with a standard deviation of
25mg per litre. She decides that she can afford a sample size of 500, but not larger,
and with this sample finds a sample mean of 632mg of lead per litre. The 95%
confidence interval for the mean lead content per litre of waste water produced by her
company then is:
a. (630.25, 633.75)
b. (639.25, 642.75)
*c. (629.81, 634.19)
d. (630.04, 633.96)
e. (630.69, 633.31)
33. A researcher wants to investigate the amount of lead per litre of waste water
produced by her company. She plans to use statistical methods to estimate the
population mean of lead content per litre of water. Based on previous recordings she
assumes that the lead content is normally distributed with a standard deviation of
20mg per litre. She decides that she can afford a sample size of 400, but not larger,
and with this sample finds a sample mean of 632mg of lead per litre. The 95%
confidence interval for the mean lead content per litre of waste water produced by her
company then is:
a. (630.25, 633.75)
b. (639.25, 642.75)
c. (629.81, 634.19)
*d. (630.04, 633.96)
e. (630.69, 633.31)
34. A researcher wants to investigate the amount of lead per litre of waste water
produced by her company. She plans to use statistical methods to estimate the
population mean of lead content per litre of water. Based on previous recordings she
assumes that the lead content is normally distributed with a standard deviation of
15mg per litre. She decides that she can afford a sample size of 500, but not larger,
and with this sample finds a sample mean of 632mg of lead per litre. The 95%
confidence interval for the mean lead content per litre of waste water produced by her
company then is:
a. (630.25, 633.75)
b. (639.25, 642.75)
c. (629.81, 634.19)
d. (630.04, 633.96)
*e. (630.69, 633.31)
35. Suppose that a random sample of 50 bottles of a particular brand of cough
medicine is selected and the alcohol content of each bottle measured. The sample
mean alcohol content is 8.6 ml with a population standard deviation of 2.88ml.
Calculate a 99% confidence interval for the true mean alcohol content for the
population of all bottles of the brand under study.
*a. (7.55, 9.65)
b. (8.15, 10.25)
c. (7.49, 9.71)
d. (7.43, 9.77)
e. (7.68, 9.52)
36. Suppose that a random sample of 50 bottles of a particular brand of cough
medicine is selected and the alcohol content of each bottle measured. The sample
mean alcohol content is 9.2 ml with a population standard deviation of 2.88ml.
Calculate a 99% confidence interval for the true mean alcohol content for the
population of all bottles of the brand under study.
a. (7.55, 9.65)
*b. (8.15, 10.25)
c. (7.49, 9.71)
d. (7.43, 9.77)
e. (7.68, 9.52)
37. Suppose that a random sample of 50 bottles of a particular brand of cough
medicine is selected and the alcohol content of each bottle measured. The sample
mean alcohol content is 8.6 ml with a population standard deviation of 3.06ml.
Calculate a 99% confidence interval for the true mean alcohol content for the
population of all bottles of the brand under study.
a. (7.55, 9.65)
b. (8.15, 10.25)
*c. (7.49, 9.71)
d. (7.43, 9.77)
e. (7.68, 9.52)
38. Suppose that a random sample of 40 bottles of a particular brand of cough
medicine is selected and the alcohol content of each bottle measured. The sample
mean alcohol content is 8.6 ml with a population standard deviation of 2.88ml.
Calculate a 99% confidence interval for the true mean alcohol content for the
population of all bottles of the brand under study.
a. (7.55, 9.65)
b. (8.15, 10.25)
c. (7.49, 9.71)
*d. (7.43, 9.77)
e. (7.68, 9.52)
39. Suppose that a random sample of 50 bottles of a particular brand of cough
medicine is selected and the alcohol content of each bottle measured. The sample
mean alcohol content is 8.6 ml with a population standard deviation of 2.54ml.
Calculate a 99% confidence interval for the true mean alcohol content for the
population of all bottles of the brand under study.
a. (7.55, 9.65)
b. (8.15, 10.25)
c. (7.49, 9.71)
d. (7.43, 9.77)
*e. (7.68, 9.52)
40. Your statistics lecturer wants you to determine a confidence interval estimate for
the mean test mark for the next test. In the past, the test marks have been normally
distributed with a population standard deviation of 30.9. A 95% confidence interval
estimate if your class has 30 students and a sample mean mark of 74.2 is:
*a. 63.14 to 85.26
b. 65.18 to 83.22
c. 65.63 to 82.77
d. 64.14 to 84.26
e. 68.14 to 80.26
41. Your statistics lecturer wants you to determine a confidence interval estimate for
the mean test mark for the next test. In the past, the test marks have been normally
distributed with a population standard deviation of 25.2. A 95% confidence interval
estimate if your class has 30 students and a sample mean mark of 74.2 is:
a. 63.14 to 85.26
*b. 65.18 to 83.22
c. 65.63 to 82.77
d. 64.14 to 84.26
e. 68.14 to 80.26
42. Your statistics lecturer wants you to determine a confidence interval estimate for
the mean test mark for the next test. In the past, the test marks have been normally
distributed with a population standard deviation of 30.9. A 95% confidence interval
estimate if your class has 50 students and a sample mean mark of 74.2 is:
a. 63.14 to 85.26
b. 65.18 to 83.22
*c. 65.63 to 82.77
d. 64.14 to 84.26
e. 68.14 to 80.26
43. Your statistics lecturer wants you to determine a confidence interval estimate for
the mean test mark for the next test. In the past, the test marks have been normally
distributed with a population standard deviation of 28.1. A 95% confidence interval
estimate if your class has 30 students and a sample mean mark of 74.2 is:
a. 63.14 to 85.26
b. 65.18 to 83.22
c. 65.63 to 82.77
*d. 64.14 to 84.26
e. 68.14 to 80.26
44. Your statistics lecturer wants you to determine a confidence interval estimate for
the mean test mark for the next test. In the past, the test marks have been normally
distributed with a population standard deviation of 30.9. A 95% confidence interval
estimate if your class has 100 students is and a sample mean mark of 74.2:
a. 63.14 to 85.26
b. 65.18 to 83.22
c. 65.63 to 82.77
d. 64.14 to 84.26
*e. 68.14 to 80.26
45. An economist is interested in studying the monthly incomes of consumers in a
particular region. The population standard deviation of monthly income is known to
be R1000. A random sample of 50 individuals resulted in an average monthly income
of R15000. What is the upper end point in a 99% confidence interval for the average
monthly income in this region?
*a. R15364
b. R15328
c. R15347
d. R15382
e. R15332
46. An economist is interested in studying the monthly incomes of consumers in a
particular region. The population standard deviation of monthly income is known to
be R900. A random sample of 50 individuals resulted in an average monthly income
of R15000. What is the upper end point in a 99% confidence interval for the average
monthly income in this region?
a. R15364
*b. R15328
c. R15347
d. R15382
e. R15332
47. An economist is interested in studying the monthly incomes of consumers in a
particular region. The population standard deviation of monthly income is known to
be R1000. A random sample of 55 individuals resulted in an average monthly income
of R15000. What is the upper end point in a 99% confidence interval for the average
monthly income in this region?
a. R15364
b. R15328
*c. R15347
d. R15382
e. R15332
48. An economist is interested in studying the monthly incomes of consumers in a
particular region. The population standard deviation of monthly income is known to
be R1050. A random sample of 50 individuals resulted in an average monthly income
of R15000. What is the upper end point in a 99% confidence interval for the average
monthly income in this region?
a. R15364
b. R15328
c. R15347
*d. R15382
e. R15332
49. An economist is interested in studying the monthly incomes of consumers in a
particular region. The population standard deviation of monthly income is known to
be R1000. A random sample of 60 individuals resulted in an average monthly income
of R15000. What is the upper end point in a 99% confidence interval for the average
monthly income in this region?
a. R15364
b. R15328
c. R15347
d. R15382
*e. R15332
50. On the basis of a random sample of 100 men from a particular province in South
Africa, a 95% confidence interval for the mean height of men in the province is found
to be (177.22 cm ; 179.18 cm). What is the value of the sample mean for this sample?
*a. 178.20cm
b. 179.24cm
c. 177.38cm
d. 178.42cm
e. 176.58cm
51. On the basis of a random sample of 100 men from a particular province in South
Africa, a 95% confidence interval for the mean height of men in the province is found
to be (178.54 cm ; 179.94 cm). What is the value of the sample mean for this sample?
a. 178.20cm
*b. 179.24cm
c. 177.38cm
d. 178.42cm
e. 176.58cm
52. On the basis of a random sample of 100 men from a particular province in South
Africa, a 95% confidence interval for the mean height of men in the province is found
to be (176.50 cm ; 178.26 cm). What is the value of the sample mean for this sample?
a. 178.20cm
b. 179.24cm
*c. 177.38cm
d. 178.42cm
e. 176.58cm
53. On the basis of a random sample of 100 men from a particular province in South
Africa, a 95% confidence interval for the mean height of men in the province is found
to be (177.89 cm ; 178.95 cm). What is the value of the sample mean for this sample?
a. 178.20cm
b. 179.24cm
c. 177.38cm
*d. 178.42cm
e. 176.58cm
54. On the basis of a random sample of 100 men from a particular province in South
Africa, a 95% confidence interval for the mean height of men in the province is found
to be (175.90 cm ; 177.25 cm). What is the value of the sample mean for this sample?
a. 178.20cm
b. 179.24cm
c. 177.38cm
d. 178.42cm
*e. 176.58cm
55. On the basis of a random sample of 100 men from a particular province in South
Africa, a 95% confidence interval for the mean height of men in the province is found
to be (177.22 cm ; 179.18 cm). What is the value of the standard deviation of the
population from which this sample was drawn?
*a. 5.0
b. 3.6
c. 4.5
d. 2.7
e. 3.4
56. On the basis of a random sample of 100 men from a particular province in South
Africa, a 95% confidence interval for the mean height of men in the province is found
to be (178.54 cm ; 179.94 cm). What is the value of the standard deviation of the
population from which this sample was drawn?
a. 5.0
*b. 3.6
c. 4.5
d. 2.7
e. 3.4
57. On the basis of a random sample of 100 men from a particular province in South
Africa, a 95% confidence interval for the mean height of men in the province is found
to be (176.50 cm ; 178.26 cm). What is the value of the standard deviation of the
population from which this sample was drawn?
a. 5.0
b. 3.6
*c. 4.5
d. 2.7
e. 3.4
58. On the basis of a random sample of 100 men from a particular province in South
Africa, a 95% confidence interval for the mean height of men in the province is found
to be (177.89 cm ; 178.95 cm). What is the value of the standard deviation of the
population from which this sample was drawn?
a. 5.0
b. 3.6
c. 4.5
*d. 2.7
e. 3.4
59. On the basis of a random sample of 100 men from a particular province in South
Africa, a 95% confidence interval for the mean height of men in the province is found
to be (175.90 cm ; 177.25 cm). What is the value of the standard deviation of the
population from which this sample was drawn?
a. 5.0
b. 3.6
c. 4.5
d. 2.7
*e. 3.4
60. In developing a 95% confidence interval estimate for a population mean, the
interval estimate was (62.84; 69.46). What was the sample mean?
*a. 66.15
b. 65.83
c. 65.35
d. 67.01
e. 66.87
61. In developing a 95% confidence interval estimate for a population mean, the
interval estimate was (63.54; 68.12). What was the sample mean?
a. 66.15
*b. 65.83
c. 65.35
d. 67.01
e. 66.87
62. In developing a 95% confidence interval estimate for a population mean, the
interval estimate was (62.15; 68.55). What was the sample mean?
a. 66.15
b. 65.83
*c. 65.35
d. 67.01
e. 66.87
63. In developing a 95% confidence interval estimate for a population mean, the
interval estimate was (64.78; 69.23). What was the sample mean?
a. 66.15
b. 65.83
c. 65.35
*d. 67.01
e. 66.87
64. In developing a 95% confidence interval estimate for a population mean, the
interval estimate was (65.33; 68.41). What was the sample mean?
a. 66.15
b. 65.83
c. 65.35
d. 67.01
*e. 66.87
65. In developing a 95% confidence interval estimate for a population mean, the
interval estimate was (62.84; 69.46). Given a sample size of 100, what was the
population standard deviation?
*a. 16.89
b. 11.68
c. 16.33
d. 11.35
e. 7.86
66. In developing a 95% confidence interval estimate for a population mean, the
interval estimate was (63.54; 68.12). Given a sample size of 100, what was the
population standard deviation?
a. 16.89
*b. 11.68
c. 16.33
d. 11.35
e. 7.86
67. In developing a 95% confidence interval estimate for a population mean, the
interval estimate was (62.15; 68.55). Given a sample size of 100, what was the
population standard deviation?
a. 16.89
b. 11.68
*c. 16.33
d. 11.35
e. 7.86
68. In developing a 95% confidence interval estimate for a population mean, the
interval estimate was (64.78; 69.23). Given a sample size of 100, what was the
population standard deviation?
a. 16.89
b. 11.68
c. 16.33
*d. 11.35
e. 7.86
69. In developing a 95% confidence interval estimate for a population mean, the
interval estimate was (65.33; 68.41). Given a sample size of 100, what was the
population standard deviation?
a. 16.89
b. 11.68
c. 16.33
d. 11.35
*e. 7.86
70. In developing an interval estimate for a population mean, the population standard
deviation was assumed to be 10. The interval estimate was 50.92 ± 2.14. Had the
population standard deviation been 20, what would the interval estimate be?
a. 60.92 ± 2.14
b. 50.92 ± 12.14
c. 101.84 ± 4.28
d. 101.94 ± 12.14
*e. 50.92 ± 4.28
71. In developing an interval estimate for a population mean, the population standard
deviation was assumed to be 5. The interval estimate was 50.92 ± 2.80. Had the
population standard deviation been 10, what would the interval estimate be?
a. 60.92 ± 2.14
*b. 50.92 ± 5.60
c. 101.84 ± 4.28
d. 101.94 ± 12.14
e. 50.92 ± 4.28
72. In developing a confidence interval for a population mean, a sample of 50
observations was used. The confidence interval was 19.76 ± 1.32. Had the sample
size been 200 instead of 50, what would the interval estimate have been?
*a. 19.76 ± 0.66
b. 19.76 ± 0.33
c. 19.76 ± 2.64
d. 19.76 ± 5.28
e. 39.52 ± 1.32
73. A student conducted a study and reported that the 95% confidence interval for the
population mean was (46; 54). He was sure that the population standard deviation was
16. What was the sample size (rounded up to the nearest whole number) used to
calculate this confidence interval?
*a. 62
b. 97
c. 110
d. 30
e. 40
74. A student conducted a study and reported that the 95% confidence interval for the
population mean was (46; 54). He was sure that the population standard deviation was
20. What was the sample size (rounded up to the nearest whole number) used to
calculate this confidence interval?
a. 62
*b. 97
c. 110
d. 30
e. 40
75. A student conducted a study and reported that the 95% confidence interval for the
population mean was (46; 52). He was sure that the population standard deviation was
16. What was the sample size (rounded up to the nearest whole number) used to
calculate this confidence interval?
a. 62
b. 97
*c. 110
d. 30
e. 40
76. A student conducted a study and reported that the 95% confidence interval for the
population mean was (46; 54). He was sure that the population standard deviation was
11. What was the sample size (rounded up to the nearest whole number) used to
calculate this confidence interval?
a. 62
b. 97
c. 110
*d. 30
e. 40
77. A student conducted a study and reported that the 95% confidence interval for the
population mean was (46; 56). He was sure that the population standard deviation was
16. What was the sample size (rounded up to the nearest whole number) used to
calculate this confidence interval?
a. 62
b. 97
c. 110
d. 30
*e. 40
78. Sand is packed into bags which are then weighed on scales. It is known that if full
bags of sand are intended to weigh μ kg, then the weight recorded by the scales will
be normally distributed with a mean μ kg and a standard deviation of 0.36kg. A
particular bag of sand was weighed four times and the weight recorded each time was
different. The sample mean weight was recorded as 34.7kg. What is the total width
of a 95% confidence interval for the true weight of the full bag of sand?
*a. 0.71kg
b. 0.36kg
c. 0.98kg
d. 0.45kg
e. 0.90kg
79. Sand is packed into bags which are then weighed on scales. It is known that if full
bags of sand are intended to weigh μ kg, then the weight recorded by the scales will
be normally distributed with a mean μ kg and a standard deviation of 0.36kg. A
particular bag of sand was weighed four times and the weight recorded each time was
different. The sample mean weight was recorded as 36.2kg. What is the total width
of a 95% confidence interval for the true weight of the full bag of sand?
*a. 0.71kg
b. 0.36kg
c. 0.98kg
d. 0.45kg
e. 0.90kg
80. Sand is packed into bags which are then weighed on scales. It is known that if full
bags of sand are intended to weigh μ kg, then the weight recorded by the scales will
be normally distributed with a mean μ kg and a standard deviation of 0.5kg. A
particular bag of sand was weighed four times and the weight recorded each time was
different. The sample mean weight was recorded as 34.7kg. What is the total width
of a 95% confidence interval for the true weight of the full bag of sand?
a. 0.71kg
b. 0.36kg
*c. 0.98kg
d. 0.45kg
e. 0.90kg
81. Sand is packed into bags which are then weighed on scales. It is known that if full
bags of sand are intended to weigh μ kg, then the weight recorded by the scales will
be normally distributed with a mean μ kg and a standard deviation of 0.36kg. A
particular bag of sand was weighed ten times and the weight recorded each time was
different. The sample mean weight was recorded as 34.7kg. What is the total width
of a 95% confidence interval for the true weight of the full bag of sand?
a. 0.71kg
b. 0.36kg
c. 0.98kg
*d. 0.45kg
e. 0.90kg
82. Sand is packed into bags which are then weighed on scales. It is known that if full
bags of sand are intended to weigh μ kg, then the weight recorded by the scales will
be normally distributed with a mean μ kg and a standard deviation of 0.36kg. A
particular bag of sand was weighed four times and the weight recorded each time was
different. The sample mean weight was recorded as 38.1kg. What is the total width
of a 95% confidence interval for the true weight of the full bag of sand?
*a. 0.71kg
b. 0.36kg
c. 0.98kg
d. 0.45kg
e. 0.90kg
83. An analyst is conducting a hypothesis test to determine if the mean time spent on
investment research by portfolio managers is different from 3 hours per day. The test
uses a random sample of 64 portfolio managers, where the sample mean time spent on
research is found to be 2.5 hours. The population standard deviation is 1.5 hours.
What is the half-width (from the middle of the confidence interval to either of the
confidence limits) of the 99% confidence interval for the population mean time spent
on investment research by portfolio managers?
*a. 0.48
b. 0.96
c. 0.64
d. 0.39
e. 0.78
84. An analyst is conducting a hypothesis test to determine if the mean time spent on
investment research by portfolio managers is different from 3 hours per day. The test
uses a random sample of 64 portfolio managers, where the sample mean time spent on
research is found to be 2.7 hours. The population standard deviation is 1.5 hours.
What is the half-width (from the middle of the confidence interval to either of the
confidence limits) of the 99% confidence interval for the population mean time spent
on investment research by portfolio managers?
*a. 0.48
b. 0.96
c. 0.64
d. 0.39
e. 0.78
85. An analyst is conducting a hypothesis test to determine if the mean time spent on
investment research by portfolio managers is different from 3 hours per day. The test
uses a random sample of 64 portfolio managers, where the sample mean time spent on
research is found to be 2.5 hours. The population standard deviation is 2 hours. What
is the half-width (from the middle of the confidence interval to either of the
confidence limits) of the 99% confidence interval for the population mean time spent
on investment research by portfolio managers?
a. 0.48
b. 0.96
*c. 0.64
d. 0.39
e. 0.78
86. An analyst is conducting a hypothesis test to determine if the mean time spent on
investment research by portfolio managers is different from 3 hours per day. The test
uses a random sample of 100 portfolio managers, where the sample mean time spent
on research is found to be 2.5 hours. The population standard deviation is 1.5 hours.
What is the half-width (from the middle of the confidence interval to either of the
confidence limits) of the 99% confidence interval for the population mean time spent
on investment research by portfolio managers?
a. 0.48
b. 0.96
c. 0.64
*d. 0.39
e. 0.78
87. An analyst is conducting a hypothesis test to determine if the mean time spent on
investment research by portfolio managers is different from 3 hours per day. The test
uses a random sample of 64 portfolio managers, where the sample mean time spent on
research is found to be 2.3 hours. The population standard deviation is 1.5 hours.
What is the half-width (from the middle of the confidence interval to either of the
confidence limits) of the 99% confidence interval for the population mean time spent
on investment research by portfolio managers?
*a. 0.48
b. 0.96
c. 0.64
d. 0.39
e. 0.78
88. A random variable, X, follows a normal distribution with a population standard
deviation of 12. A sample of size 64 is selected from this population and the sample
mean calculated as 45.23. What is the total width of a 90% confidence interval for the
true population mean in this case?
*a. 4.9
b. 6.6
c. 3.9
d. 3.3
e. 5.6
89. A random variable, X, follows a normal distribution with a population standard
deviation of 16. A sample of size 64 is selected from this population and the sample
mean calculated as 45.23. What is the total width of a 90% confidence interval for the
true population mean in this case?
a. 4.9
*b. 6.6
c. 3.9
d. 3.3
e. 5.6
90. A random variable, X, follows a normal distribution with a population standard
deviation of 12. A sample of size 100 is selected from this population and the sample
mean calculated as 45.23. What is the total width of a 90% confidence interval for the
true population mean in this case?
a. 4.9
b. 6.6
*c. 3.9
d. 3.3
e. 5.6
91. A random variable, X, follows a normal distribution with a population standard
deviation of 8. A sample of size 64 is selected from this population and the sample
mean calculated as 45.23. What is the total width of a 90% confidence interval for the
true population mean in this case?
a. 4.9
b. 6.6
c. 3.9
*d. 3.3
e. 5.6
92. A random variable, X, follows a normal distribution with a population standard
deviation of 12. A sample of size 49 is selected from this population and the sample
mean calculated as 45.23. What is the total width of a 90% confidence interval for the
true population mean in this case?
a. 4.9
b. 6.6
c. 3.9
d. 3.3
*e. 5.6
93. An economist is interested in studying the monthly incomes of consumers in a
particular region. The population standard deviation of monthly income is known to
be R1000. A random sample of 50 individuals resulted in an average monthly income
of R15000. What is the total width of the 90% confidence interval?
*a. 465
b. 419
c. 444
d. 489
e. 425
94. An economist is interested in studying the monthly incomes of consumers in a
particular region. The population standard deviation of monthly income is known to
be R900. A random sample of 50 individuals resulted in an average monthly income
of R15000. What is the total width of the 90% confidence interval?
a. 465
*b. 419
c. 444
d. 489
e. 425
95. An economist is interested in studying the monthly incomes of consumers in a
particular region. The population standard deviation of monthly income is known to
be R1000. A random sample of 55 individuals resulted in an average monthly income
of R15000. What is the total width of the 90% confidence interval?
a. 465
b. 419
*c. 444
d. 489
e. 425
96. An economist is interested in studying the monthly incomes of consumers in a
particular region. The population standard deviation of monthly income is known to
be R1050. A random sample of 50 individuals resulted in an average monthly income
of R15000. What is the total width of the 90% confidence interval?
a. 465
b. 419
c. 444
*d. 489
e. 425
97. An economist is interested in studying the monthly incomes of consumers in a
particular region. The population standard deviation of monthly income is known to
be R1000. A random sample of 60 individuals resulted in an average monthly income
of R15000. What is the total width of the 90% confidence interval?
a. 465
b. 419
c. 444
d. 489
*e. 425
98. Sand is packed into bags which are then weighed on scales. It is known that if full
bags of sand are intended to weigh μ kg, then the weight recorded by the scales will
be normally distributed with a mean μ kg and a standard deviation of 0.36kg. How
many times would a full sack have to be weighed so that the estimate of the weight
would be within 0.15 kg of the true weight with 95% confidence?
*a. 23
b. 43
c. 13
d. 28
e. 18
99. Sand is packed into bags which are then weighed on scales. It is known that if full
bags of sand are intended to weigh μ kg, then the weight recorded by the scales will
be normally distributed with a mean μ kg and a standard deviation of 0.5kg. How
many times would a full sack have to be weighed so that the estimate of the weight
would be within 0.15 kg of the true weight with 95% confidence?
a. 23
*b. 43
c. 13
d. 28
e. 18
100. Sand is packed into bags which are then weighed on scales. It is known that if
full bags of sand are intended to weigh μ kg, then the weight recorded by the scales
will be normally distributed with a mean μ kg and a standard deviation of 0.36kg.
How many times would a full sack have to be weighed so that the estimate of the
weight would be within 0.2 kg of the true weight with 95% confidence?
a. 23
b. 43
*c. 13
d. 28
e. 18
101. Sand is packed into bags which are then weighed on scales. It is known that if
full bags of sand are intended to weigh μ kg, then the weight recorded by the scales
will be normally distributed with a mean μ kg and a standard deviation of 0.4kg. How
many times would a full sack have to be weighed so that the estimate of the weight
would be within 0.15 kg of the true weight with 95% confidence?
a. 23
b. 43
c. 13
*d. 28
e. 18
102. Sand is packed into bags which are then weighed on scales. It is known that if
full bags of sand are intended to weigh μ kg, then the weight recorded by the scales
will be normally distributed with a mean μ kg and a standard deviation of 0.36kg.
How many times would a full sack have to be weighed so that the estimate of the
weight would be within 0.17 kg of the true weight with 95% confidence?
a. 23
b. 43
c. 13
d. 28
*e. 18
103. A researcher wants to investigate the amount of lead per litre of waste water
produced by her company. She plans to use statistical methods to estimate the
population mean of lead content per litre of water. Based on previous recordings she
assumes that the lead content is normally distributed with a standard deviation of
20mg per litre. How large a sample should she take to estimate the mean lead content
per litre of water to within 1mg with 95% confidence?
*a. 1537
b. 865
c. 385
d. 2401
e. 97
104. A researcher wants to investigate the amount of lead per litre of waste water
produced by her company. She plans to use statistical methods to estimate the
population mean of lead content per litre of water. Based on previous recordings she
assumes that the lead content is normally distributed with a standard deviation of
15mg per litre. How large a sample should she take to estimate the mean lead content
per litre of water to within 1mg with 95% confidence?
a. 1537
*b. 865
c. 385
d. 2401
e. 97
105. A researcher wants to investigate the amount of lead per litre of waste water
produced by her company. She plans to use statistical methods to estimate the
population mean of lead content per litre of water. Based on previous recordings she
assumes that the lead content is normally distributed with a standard deviation of
20mg per litre. How large a sample should she take to estimate the mean lead content
per litre of water to within 2mg with 95% confidence?
a. 1537
b. 865
*c. 385
d. 2401
e. 97
106. A researcher wants to investigate the amount of lead per litre of waste water
produced by her company. She plans to use statistical methods to estimate the
population mean of lead content per litre of water. Based on previous recordings she
assumes that the lead content is normally distributed with a standard deviation of
25mg per litre. How large a sample should she take to estimate the mean lead content
per litre of water to within 1mg with 95% confidence?
a. 1537
b. 865
c. 385
*d. 2401
e. 97
107. A researcher wants to investigate the amount of lead per litre of waste water
produced by her company. She plans to use statistical methods to estimate the
population mean of lead content per litre of water. Based on previous recordings she
assumes that the lead content is normally distributed with a standard deviation of
20mg per litre. How large a sample should she take to estimate the mean lead content
per litre of water to within 4mg with 95% confidence?
a. 1537
b. 865
c. 385
d. 2401
*e. 97
108. The financial aid officer at a certain South African university wishes to estimate
the mean cost of textbooks per semester for students. For the estimate to be useful it
should be within R30 of the true population mean. How large a sample should be used
in order to be 95% confident of achieving this level of accuracy if we know the
population standard deviation is R100.
*a. 43
b. 35
c. 97
d. 52
e. 25
109. The financial aid officer at a certain South African university wishes to estimate
the mean cost of textbooks per semester for students. For the estimate to be useful it
should be within R30 of the true population mean. How large a sample should be used
in order to be 95% confident of achieving this level of accuracy if we know the
population standard deviation is R90.
a. 43
*b. 35
c. 97
d. 52
e. 25
110. The financial aid officer at a certain South African university wishes to estimate
the mean cost of textbooks per semester for students. For the estimate to be useful it
should be within R20 of the true population mean. How large a sample should be used
in order to be 95% confident of achieving this level of accuracy if we know the
population standard deviation is R100.
a. 43
b. 35
*c. 97
d. 52
e. 25
111. The financial aid officer at a certain South African university wishes to estimate
the mean cost of textbooks per semester for students. For the estimate to be useful it
should be within R30 of the true population mean. How large a sample should be used
in order to be 95% confident of achieving this level of accuracy if we know the
population standard deviation is R110.
a. 43
b. 35
c. 97
*d. 52
e. 25
112. The financial aid officer at a certain South African university wishes to estimate
the mean cost of textbooks per semester for students. For the estimate to be useful it
should be within R40 of the true population mean. How large a sample should be used
in order to be 95% confident of achieving this level of accuracy if we know the
population standard deviation is R100.
a. 43
b. 35
c. 97
d. 52
*e. 25
113. If a random variable, X, follows a normal distribution with a variance of 25,
what sample size should be selected if a 95% confidence interval for the mean is to be
calculated to within 2 units of the true population mean?
*a. 25
b. 62
c. 11
d. 35
e. 97
114. If a random variable, X, follows a normal distribution with a variance of 64,
what sample size should be selected if a 95% confidence interval for the mean is to be
calculated to within 2 units of the true population mean?
a. 25
*b. 62
c. 11
d. 35
e. 97
115. If a random variable, X, follows a normal distribution with a variance of 25,
what sample size should be selected if a 95% confidence interval for the mean is to be
calculated to within 3 units of the true population mean?
a. 25
b. 62
*c. 11
d. 35
e. 97
116. If a random variable, X, follows a normal distribution with a variance of 36,
what sample size should be selected if a 95% confidence interval for the mean is to be
calculated to within 2 units of the true population mean?
a. 25
b. 62
c. 11
*d. 35
e. 97
117. If a random variable, X, follows a normal distribution with a variance of 25,
what sample size should be selected if a 95% confidence interval for the mean is to be
calculated to within 1 unit of the true population mean?
a. 25
b. 62
c. 11
d. 35
*e. 97
118. A retail banker working at Nedbank wishes to estimate the mean monthly credit
card expenditure of all Nedbank credit card holders. For the estimate to be useful it
should be within R100 of the true population mean. How large a sample should be
used in order to be 95% confident of achieving this level of accuracy if we know the
population standard deviation is R150.
*a. 9
b. 14
c. 6
d. 35
e. 25
119. A retail banker working at Nedbank wishes to estimate the mean monthly credit
card expenditure of all Nedbank credit card holders. For the estimate to be useful it
should be within R80 of the true population mean. How large a sample should be
used in order to be 95% confident of achieving this level of accuracy if we know the
population standard deviation is R150.
a. 9
*b. 14
c. 6
d. 35
e. 25
120. A retail banker working at Nedbank wishes to estimate the mean monthly credit
card expenditure of all Nedbank credit card holders. For the estimate to be useful it
should be within R100 of the true population mean. How large a sample should be
used in order to be 95% confident of achieving this level of accuracy if we know the
population standard deviation is R120.
a. 9
b. 14
*c. 6
d. 35
e. 25
121. A retail banker working at Nedbank wishes to estimate the mean monthly credit
card expenditure of all Nedbank credit card holders. For the estimate to be useful it
should be within R50 of the true population mean. How large a sample should be
used in order to be 95% confident of achieving this level of accuracy if we know the
population standard deviation is R150.
a. 9
b. 14
c. 6
*d. 35
e. 25
122. A retail banker working at Nedbank wishes to estimate the mean monthly credit
card expenditure of all Nedbank credit card holders. For the estimate to be useful it
should be within R100 of the true population mean. How large a sample should be
used in order to be 95% confident of achieving this level of accuracy if we know the
population standard deviation is R250.
a. 9
b. 14
c. 6
d. 35
*e. 25