Student name:__________
MULTIPLE CHOICE - Choose the one alternative that best completes the statement or
answers the question.
1) i. It is often not feasible to study the entire population because it is impossible to check all
the items in the population.
ii. Sampling a population is often necessary because the cost of studying all the items in the
population is prohibitive.
iii. Sampling is a sign of laziness on the part of the statistician.
A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.
2) i. A simple random sample assumes that each item or person in the population has an equal
chance of being included.
ii. We can expect some difference between sample statistics and the corresponding
population parameters. This difference is called the sampling error.
iii. A sampling distribution of the means is a probability distribution consisting of a list of all
possible sample means of a given sample size selected from a population and the probability
of occurrence associated with each sample mean.
A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.
3) i. If probability sampling is done, each item in the population has a chance of being chosen.
ii. If the size of a sample equals the size of the population, we would not expect any error in
estimating the population parameter.
A) (i) and (ii) are both correct statements.
B) (i) is correct but not (ii).
C) (ii) is correct but not (i).
D) (i) and (ii) are both false statements.
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4) What is it called when all the items in a population have a chance of being selected in a
sample?
A) Random sampling
B) z-score
C) Sampling error
D) Non probability sampling
5) Manufacturers were subdivided into groups by volume of sales. Those with more than $100
million in sales were classified as Class A large; those from $50 to $100 million as Class A
medium size; and those between $25 and $50 million, and so on. Samples were then selected
from each of these groups. What is this type of sampling called?
A) Simple random
B) Stratified random
C) Cluster
D) Systematic
6) Suppose we select every fifth invoice in a file. What type of sampling is this?
A) Simple random
B) Stratified random
C) Cluster
D) Systematic
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7) We wish to study the advertising expenditures for the 200 largest companies in Canada.
Suppose the objective of the study is to determine whether firms with high returns on equity
(a measure of profitability) spent more of each sales dollar on advertising than firms with a
low return or deficit. To make sure that the sample is a fair representation of the 200
companies, the companies are grouped on percent return on equity
Stratum
Profitability (return on
equity)
1
30% and over
4
0.02
1*
2
20 up to 30%
20
0.10
5*
3
10 up to 20%
108
0.54
27
4
0 up to 10%
66
0.33
16
5
Deficit
2
0.01
1
200
1.00
50
Total
Number of
Firms
Relative
Frequency
Number
Sampled
What is this type of sampling called?
A) Simple random
B) Stratified random
C) Cluster
D) Systematic
8) What is the difference between a sample mean and the population mean called?
A) Standard error of the mean
B) Sampling error
C) Interval estimate
D) Point estimate
9) Suppose we select every tenth invoice in a file. What type of sampling is this?
A) Random
B) Cluster
C) Stratified
D) Systematic
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10) A province-wide sample survey is to be made. First, the province is subdivided into counties.
Seven counties are selected at random and further sampling is concentrated on these seven
counties. What type of sampling is this?
A) Simple random
B) Non proportional
C) Cluster
D) Stratified
11) Which of the following would be used as a point estimate for the population mean ( µ)?
A) σ
B) x/n
C)
D) s
E) p
12) Mileage tests were conducted on a randomly selected sample of 100 newly developed
automobile tires. The average tread life was found to be 80,000 kilometres with a standard
deviation of 5,600 kilometres. What is the best estimate of the average tread life in
kilometres for the entire population of these tires?
A) 80,000
B) 5,600
C) (80,000/100)
D) (5,600/100)
13) A sample mean is the best point estimate of the
A) population standard deviation.
B) population median.
C) population mean.
D) the sample standard deviation.
E) the population variance.
14) A sample standard deviation is the best point estimate of the
A) population range.
B) population skewness.
C) population mode.
D) population standard deviation.
E) population variance.
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15) Recently, a university surveyed recent graduates of the English Department for their starting
salaries. One hundred graduates returned the survey. The average salary was $35,000 with a
standard deviation of $2,000.
What is the best point estimate of the population mean?
A) $25,000
B) $2,000
C) $500
D) $400
E) $35,000
16) A confidence interval for a population mean:
A) estimates the population range.
B) estimates a likely interval for a population mean.
C) estimates a likelihood or probability.
D) estimates the population standard deviation.
17) A 95% confidence interval infers that the population mean is:
A) between 0 and 100%.
B) within ± 1.96 standard deviations of the sample mean.
C) within ± 1.96 standard errors of the sample mean.
D) within ± 1.645 standard deviations of the sample mean.
E) too large.
18) When a confidence interval for a population mean is constructed from sample data,
A) we can conclude that the population mean is in the interval.
B) we can conclude that the population mean is not in the interval.
C) we can conclude, with a stated level of confidence, that the population mean is in the
interval.
D) we cannot make any inferences.
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19) Recently, a university surveyed recent graduates of the English Department for their starting
salaries. Four hundred graduates returned the survey. The average salary was $25,000. The
population standard deviation is known to be $2,500. Interpret the results of the 95%
confidence interval.
A) The population mean is in the interval.
B) The population mean is not in the interval.
C) The likelihood that any confidence interval based on a sample of 400 graduates will
contain the population mean is 0.95.
D) There is a 95% chance that the computed interval does not contain the population
mean.
20) The z-value associated with a 90% level of confidence is:
A) 1.96
B) 1.645
C) 2.33
D) 2.575
E) 1.28
21) The z-value associated with a 94% level of confidence is:
A) 1.96
B) 1.645
C) 2.33
D) 2.575
E) 1.88
22) The z-value associated with a 96% level of confidence is:
A) 1.96
B) 1.645
C) 2.33
D) 2.05
E) 1.28
23) The z-value associated with an 80% level of confidence is:
A) 1.96
B) 1.645
C) 2.33
D) 2.575
E) 1.28
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24) i. The t distribution is based on the assumption that the population of interest is normal or
nearly normal.
ii. The t distribution is a continuous distribution.
iii. There is not one t distribution, but rather a "family" of t distributions.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.
25) i. The t distribution is based on the assumption that the population of interest is normal or
nearly normal.
ii. The t distribution is a discrete distribution.
iii. There is not one t distribution, but rather a "family" of t distributions.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.
26) i. Two examples of a hypothesis are:
1) mean monthly income from all sources for senior citizens is $841 and
2) twenty percent of juvenile offenders ultimately are caught and sentenced to prison.
ii. Hypothesis testing is a procedure based on sample evidence and probability theory to
decide whether the hypothesis is a reasonable statement.
iii. Since there is more variability in sample means computed from smaller samples, we have
more confidence in the resulting estimates and are less apt to reject null hypothesis.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.
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27) i. Two examples of a hypothesis are: 1) mean monthly income from all sources for senior
citizens is $841 and 2) twenty percent of juvenile offenders ultimately are caught and
sentenced to prison.
ii. Hypothesis testing is a procedure based on sample evidence and probability theory to
decide whether the hypothesis is a reasonable statement.
iii. The test statistic for a problem involving an unknown population standard deviation is the
Student's t distribution.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.
28) i. Two examples of a hypothesis are: 1) mean monthly income from all sources for senior
citizens is $841 and 2) twenty percent of juvenile offenders ultimately are caught and
sentenced to prison.
ii. Hypothesis testing is a procedure based on sample evidence and probability theory to
decide whether the hypothesis is a reasonable statement.
iii. We call a statement about the value of a population parameter a hypothesis.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.
29) i. Two examples of a hypothesis are:
1) mean monthly income from all sources for senior citizens is $841 and
2) twenty percent of juvenile offenders ultimately are caught and sentenced to prison.
ii. Since there is more variability in sample means computed from smaller samples, we have
more confidence in the resulting estimates and are less apt to reject null hypothesis.
iii. The test statistic for a problem where the population standard deviation is unknown is the
Student's t distribution.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.
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30) i. Two examples of a hypothesis are:
1) mean monthly income from all sources for senior citizens is $841 and
2) twenty percent of juvenile offenders ultimately are caught and sentenced to prison.
ii. Since there is more variability in sample means computed from smaller samples, we have
more confidence in the resulting estimates and are less apt to reject null hypothesis.
iii. We call a statement about the value of a population parameter a hypothesis.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.
31) Which of the following does NOT hold true for the t distribution?
A) Confidence intervals will be wider than for large samples.
B) The region of acceptance will be larger than for large samples.
C) A larger computed t value will be needed to reject the null hypothesis than for large
samples using z.
D) There is only one t distribution.
32) i. An alternate hypothesis is a statement about a population parameter that is accepted when
the null hypothesis is rejected.
ii. The level of significance is the risk we assume of rejecting the null hypothesis when it is
actually true.
iii. There is only one level of significance that is applied to all studies involving sampling.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.
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33) i. An alternate hypothesis is a statement about a population parameter that is accepted when
the null hypothesis is rejected.
ii. The level of significance is the risk we assume of rejecting the null hypothesis when it is
actually true.
iii. The researcher must decide on the level of significance before formulating a decision rule
and collecting sample data.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.
34) i. The level of significance is the risk we assume of rejecting the null hypothesis when it is
actually true.
ii. There is only one level of significance that is applied to all studies involving sampling.
iii. The researcher must decide on the level of significance before formulating a decision rule
and collecting sample data.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.
35) i. Two types of possible errors always exist when testing hypotheses—a Type I error, in
which the null hypothesis is rejected when it should not have been rejected, and a Type II
error in which the null hypothesis is not rejected when it should have been rejected.
ii. A test statistic is a value determined from sample information collected to test the null
hypothesis.
iii. The region or area of rejection defines the location of all those values that are so large or
so small that the probability of their occurrence under a true null hypothesis is rather remote.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.
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36) i. The first step in testing a hypothesis is to state the decision rule.
ii. To prevent bias, the level of significance is selected before setting up the decision rule and
sampling the population.
iii. The fifth and final step in testing a hypothesis is taking a sample and, based on the
decision rule, deciding if the null hypothesis should be rejected.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (ii) and (iii) are correct statements but not (i).
37) i. To prevent bias, the level of significance is selected before setting up the decision rule and
sampling the population.
ii. The level of significance is the probability that a true hypothesis is rejected.
iii. If the critical values of the test statistic z are ±1.96, they are the dividing points between
the areas of rejection and non-rejection.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (ii) and (iii) are correct statements but not (i).
38) The null hypothesis makes a claim about what value?
A) Population parameter
B) Sample statistic
C) Sample mean
D) Type II error
39) Which of the following is NOT one of the five steps in the hypothesis testing procedure?
A) Formulate a decision rule
B) State the null and alternate hypotheses
C) Select a level for β
D) Identify the test statistic
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40) If the alternate hypothesis states that μ does not equal 4,000, what is the rejection region for
the hypothesis test?
A) Both tails
B) Lower or left tail
C) Upper or right tail
D) Center
41) Suppose we select every tenth invoice in a file. What type of sampling is this?
A) Random
B) Cluster
C) Stratified
D) Systematic
42) A province-wide sample survey is to be made. First, the province is subdivided into counties.
Seven counties are selected at random and further sampling is concentrated on these seven
counties. What type of sampling is this?
A) Simple random
B) Non proportional
C) Cluster
D) Stratified
43) Sampling error is the difference between a corresponding sample statistic and the
A) sample mean.
B) biased sample.
C) population parameter.
D) chance error.
44) i. An estimate of the population mean based on a large sample is less reliable than an
estimate made using a small sample.
ii. The standard error of the mean will vary according to the size of the sample that is in the
denominator. As the sample size n gets larger, the variability of the sample means gets
smaller.
iii. To determine the value of the standard error of the mean, the total error is divided by the
sample size.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement, but not (ii) or (iii).
C) (ii) is a correct statement, but not (i) or (iii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.
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45) (i) As the sample size ( n) increases, the spread in the distribution of the sample means stays
the same.
(ii) If the sampling size equals the population size, the sampling error is 1.
(iii) If a population is normally distributed, the sampling distribution of the mean is normally
distributed.
A) (i), (ii), and (iii) are all correct statements.
B) (iii) is a correct statement, but not (i) or (ii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.
46) Which of the following is the standard error of the mean?
A) µ
B) x/n
C)
D) s/√n
47) All possible samples of size n are selected from a population and the mean of each sample is
determined. What is the mean of the sample means?
A) Exactly the same as the population mean
B) Larger than the population mean
C) Smaller than the population mean
D) Cannot be estimated in advance
48) The mean of all possible sample means is equal to the:
A) population variance.
B) σ2/ n.
C) sample variance.
D) population mean.
49) An experiment involves randomly selecting a sample of 256 middle managers for study. One
item of interest is their mean annual income. The sample mean is computed to be $35,420
and the sample standard deviation is $2,050. What is the standard error of the mean?
A) $5.65
B) $128.13
C) $138.36
D) $2,050
E) $8.01
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50) A group of statistics students decided to conduct a survey at their university to find the
average (mean) amount of time students spend studying per week. Based on a simple random
sample, they surveyed 144 students. The statistics showed that students studied an average of
20 hours per week with a standard deviation of 10 hours.
What is the standard error of the mean?
A) 0.83
B) 10
C) 0.5
D) 2
51) i. The t distribution is positively skewed.
ii. All t distributions have the same mean of zero and a standard deviation of 1.
iii. The t distribution is more spread out and flatter at the center than is the standard normal
distribution. However, as the sample size increases, the t distribution curve approaches the
standard normal distribution.
A) (i), (ii), and (iii) are all correct statements.
B) (iii) is a correct statement but not (i) or (ii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.
52) i. The Student t distribution has a greater spread than does the z distribution. As a result, the
critical values of t for a given level of significance are larger in magnitude than the
corresponding z critical values.
ii. The test statistic t has n-1 degrees of freedom.
iii. William S. Gosset, a brewmaster, developed the t test for the Guinness Brewery in
Ireland, who published it in 1908 using the pen name "Student."
A) (i), (ii), and (iii) are all correct statements.
B) (iii) is a correct statement but not (i) or (ii).
C) (i) and,(iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.
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53) i. The test statistic t has n-1 degrees of freedom.
ii. All t distributions have the same mean of zero and a standard deviation of 1.
iii. The t distribution is more spread out and flatter at the center than is the standard normal
distribution. However, as the sample size increases, the t distribution curve approaches the
standard normal distribution.
A) (i), (ii), and (iii) are all correct statements.
B) (iii) is a correct statement but not (i) or (ii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.
54) i. The test statistic for a problem involving an unknown population standard deviation is the
Student's t distribution.
ii. The t distribution approaches the Z distribution as the sample size increases.
iii. As the sample size increases, the computed value of t decreases.
A) (i), (ii), and (iii) are all correct statements.
B) (iii) is a correct statement but not (i) or (ii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.
55) Which statement is correct about the t distribution?
A) Mean = 0
B) Symmetric
C) Based on degrees of freedom
D) Mean = 0, symmetric and based on degrees of freedom
E) Mean = 0 and symmetric
56) What kind of distribution is the t distribution?
A) Continuous
B) Discrete
C) Subjective
D) Standard
57) How does the t distribution differ from the standard z distribution?
A) Continuous distribution
B) Bell-shaped
C) Family of distributions
D) Symmetrical
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58) A sample of 20 is selected from the population. What is the number of degrees of freedom
used to determine the appropriate critical t-value?
A) 20
B) 19
C) 21
D) 25
59) The t distribution is similar to the z distribution in all BUT ONE of the following
characteristics. Which one is it?
A) Continuous
B) Symmetrical
C) Bell-shaped
D) t distribution's mean = 0 and standard deviation = 1
60) Student's t is used when
A) the sample is more than 30 observations.
B) the sample size is ≤ 5% of the population.
C) the population standard deviation is unknown.
D) any time.
61) The distribution of Student's t has
A) a mean of zero and a standard deviation of one.
B) a mean of one and a standard deviation of one.
C) a mean of zero and a standard deviation that depends on the sample size.
D) a mean that depends on the sample size and a standard deviation of one.
62) The distribution of Student's t is
A) symmetrical.
B) negatively skewed.
C) positively skewed.
D) a discrete probability distribution.
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63) When using Student's t to compute an interval estimate,
A) we assume that the samples are collected from normally distributed populations.
B) we estimate the population standard deviation based on the sample standard
deviation.
C) use the z distribution.
D) we assume that samples are collected from normally distributed populations and the
estimate of the population standard deviation based on the sample standard deviation.
E) we assume that the samples are collected from normally distributed populations and
use the z distribution.
64) The t distribution approaches __________ as the sample size increases. As the sample size
increases, the computed value of t _________.
A) Z distribution; decreases
B) Z distribution; increases
C) Z distribution; stays the same
D) 0; decreases
E) 0; increases
65) In order to construct a 90% confidence interval for the population mean when the population
standard deviation is unknown and the sample size is 18, you should use the t-value indicated
as:
A) t0.10,18
B) t 0.10,17
C) t0.05,18
D) t0.05,17
E) t0.90,17
66) In order to construct a 95% confidence interval for the population mean when the population
standard deviation is unknown and the sample size is 15, you should use the t-value indicated
as:
A) t0.10,15
B) t0.10,14
C) t0.05,15
D) t0.05,14
E) t0.025,14
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67) A sample of 100 students is selected from a known population of 1,000 students to construct
a 95% confidence interval for the average SAT score. What correction factor should be used
to compute the standard error?
A) 0.949
B) 0.901
C) 1.96
D) 9.01
E) Cannot be determined
68) The mean weight of trucks traveling on a particular section of Highway 401 is not known. A
provincial highway inspector needs an estimate of the mean. He selects a random sample of
49 trucks passing the weighing station and finds the mean is 15.8 tons, with a standard
deviation of the sample of 3.8 tons. What is the 95 percent interval for the population mean?
A) 14.7 and 16.9
B) 13.2 and 17.6
C) 10.0 and 20.0
D) 16.1 and 18.1
69) The Dean of the Business School wants to estimate the mean number of hours worked per
week by students. A sample of only 12 students showed a mean of 24 hours with a standard
deviation of 4 hours. Find the 95 percent confidence interval for the population mean.
A) 21.46 and 26.54
B) 21.17 and 26.45
C) 22.88 and 25.12
D) 21.07 and 26.07
E) 21.93 and 26.07
70) The manager of the college cafeteria wants to estimate the mean amount spent per customer
per purchase. A sample of 10 customers revealed the following amounts spent:
$4.45
$4.05
$4.95
$3.25
$4.68
$5.75
$6.01
$3.99
$5.25
$2.95
Find the 99 percent confidence limits for the mean amount spent.
Sample mean = $4.53, s = $1.00
A) 3.53 and 5.53
B) 3.50 and 5.56
C) 3.48 and 5.58
D) 3.84 and 5.85
E) 3.35 and 5.35
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71) A sample of 500 executives who own their own home revealed 175 planned to sell their
homes and retire to Victoria. Develop a 98% confidence interval for the proportion of
executives that plan to sell and move to Victoria.
A) 30% and 40%
B) 29% and 41%
C) 28% and 42%
D) 29.5% and 40.5%
E) 29.3% and 41.3%
72) What are the two rejection areas in using a two-tailed test and the 0.01 level of significance
when the population standard deviation is known?
A) Above 1.96 and below -1.96
B) Above 1.65 and below -1.65
C) Above 2.58 and below -2.58
D) Above 1.00 and below -1.00
73) What are the critical z-values for a two-tailed hypothesis test if α = 0.01?
A) ±1.96
B) ±2.33
C) ±2.58
D) ±1.65
74) i. If the null hypothesis is μ≥ 200 and the alternate hypothesis states that μ is less than 200,
then, a two-tail test is being conducted.
ii. For a one-tailed test of hypothesis, the area of rejection is only in one tail of the curve.
iii. As the sample size increases, the curve of the t-distribution approaches the standard
normal distribution
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.
75) If the alternative hypothesis states that μ > 6,700, what is the rejection region for the
hypothesis test?
A) Both tails
B) Lower tail
C) Upper tail
D) Center
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76) A random sample of size 15 is selected from a normal population. The population standard
deviation is unknown. Assume that a two-tailed test at the 0.10 significance level is to be
used. For what value of t will the null hypothesis be rejected?
A) To the left of -1.282 or to the right of 1.282
B) To the left of -1.345 or to the right of 1.345
C) To the left of -1.761 or to the right of 1.761
D) To the left of -1.645 or to the right of 1.645
77) What is the critical value for a right-tailed hypothesis test in which a null hypothesis is tested
at the 5% level of significance based on a sample size of 25 and an unknown population
standard deviation?
A) 1.708
B) 1.711
C) 2.060
D) 2.064
78) Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally
distributed with a mean of 35,600 kilometres. A manufacturer of spark plugs claims that its
plugs have an average life in excess of 35,600 kilometres. The fleet owner purchased 18 sets
and found that the sample average life was 37,700 kilometres, the sample standard deviation
was 2415 kilometres and the computed t = 3.677.
A) Based on these findings, there is enough evidence to accept the manufacturer's claim
at the 0.05 level.
B) Based on these findings, there is NOT enough evidence to accept the manufacturer's
claim at the 0.05 level.
C) Based on these findings, there is enough evidence to accept the manufacturer's claim
at the 0.05 level, but NOT at the 0.01 level.
D) Based on these findings, there is NOT enough evidence to accept the manufacturer's
claim at the 0.01 level.
E) Based on these findings, there in NOT enough evidence to accept the manufacturer's
claim at either the 0.05 or the 0.01 level.
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79) i. For a one-tailed test using the 0.05 level of significance, the critical value for the z test is
1.645, but for t it is 1.96.
ii. For a one-tailed test using the 0.01 level of significance, the critical value for the z-test is
1.645, but for t it is 1.96.
iii. For a two-tailed test using the 0.05 level of significance the critical value for the z-test is
1.96 and it is the same for the t-test.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.
80) The mean length of a small counter balance bar is 43 millimeters. There is concern that the
adjustments of the machine producing the bars have changed. Test the claim at the 0.02 level
that there has been no change in the mean length. The alternate hypothesis is that there has
been a change. Twelve bars ( n = 12) were selected at random and their lengths recorded. The
lengths are (in millimeters) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43 and 42. The mean of the
sample is 41.5 and the standard deviation 1.784. Computed t = -2.913. Has there been a
statistically significant change in the mean length of the bars?
A) Yes, because the computed t lies in the area beyond the critical.
B) No, because the information given is not complete.
C) No, because the computed t lies in the area to the right of -2.718.
81) From past records it is known that the average life of a battery used in a digital clock is 305
days. The battery life is normally distributed. The battery was recently modified to last
longer. A sample of 20 of the modified batteries was tested. It was discovered that the mean
life was 311 days and the sample standard deviation was 12 days. We want to test at the 0.05
level of significance whether the modification increases the life of the battery. What is our
decision rule?
A) Do not reject the null hypothesis if computed t is 1.96 or greater
B) Reject the null hypothesis if computed t is less than 1.96
C) Do not reject the null hypothesis if computed t is 1.729 or greater
D) Reject the null hypothesis if computed t is 2.086 or greater
E) Reject the null hypothesis if the computed t is 1.729 or greater
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82) A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate
that the average shelf life of the mix is 216 days. After a revised mix has been developed, a
sample of nine boxes of cake mix gave these shelf lives (in days): 215, 217, 218, 219, 216,
217, 217, 218 and 218. At the 0.025 level, has the shelf life of the cake mix increased?
A) Yes, because computed t is greater than the critical value.
B) Yes, because computed t is less than the critical value.
C) No, because computed t lies in the region of acceptance.
D) No, because 217.24 is quite close to 216.
83) A manufacturer wants to increase the absorption capacity of a sponge. Based on past data,
the average sponge could absorb 103.5ml. After the redesign, the absorption amounts of a
sample of sponges were (in millilitres): 121.3, 109.2, 97.6, 103.5, 112.4, 115.3, 106.5, 112.4,
118.3, and 115.3. What is the decision rule at the 0.01 level of significance to test if the new
design increased the absorption amount of the sponge?
A) Do not reject null hypothesis if computed t is less than 2.580
B) Do not reject null hypothesis if computed t is less than 2.821
C) Reject null hypothesis if computed z is 1.96 or larger
D) Reject null hypothesis if computed t is less than 2.764
84) A machine is set to fill the small size packages of Smarties candies with 56 candies per bag.
A sample revealed: 3 bags of 56, 2 bags of 57, 1 bag of 55, and 2 bags of 58. How many
degrees of freedom are there?
A) 9
B) 1
C) 8
D) 7
85) What is the critical value for t in a one-tailed hypothesis test in which a null hypothesis is
tested at the 5% level of significance based on a sample size of 15?
A) 1.708
B) 1.711
C) 1.761
D) 2.145
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Answer Key
Test name: Test 3 Statistical Concepts1310
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
B
A
A
A
B
D
B
B
D
C
C
A
C
D
E
B
C
C
C
B
E
D
E
A
C
D
A
A
C
C
D
D
A
C
A
E
A
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38)
39)
40)
41)
42)
43)
44)
45)
46)
47)
48)
49)
50)
51)
52)
53)
54)
55)
56)
57)
58)
59)
60)
61)
62)
63)
64)
65)
66)
67)
68)
69)
70)
71)
72)
73)
74)
75)
76)
77)
A
C
A
D
C
C
C
B
D
A
D
B
A
B
A
C
A
D
A
C
B
D
C
C
A
D
B
D
E
A
A
A
B
A
C
C
D
C
C
B
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78)
79)
80)
81)
82)
83)
84)
85)
A
E
A
E
A
B
D
C
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