STAT 3321 – Exam 2, Spring, 2007 – White Exam - Printed Name_______________________
1. The values of the sample mean and their probabilities that result from taking random samples is called
a(n)
a. sampling distribution
b. mean
c. median
d. standard deviation
e. binomial distribution
2. What is a requirement of all confidence intervals and hypothesis tests?
a. green medians
b. confusing material (hint: wrong answer)
c. large standard deviations
d. small sample sizes
e. simple random sample
3. In order for the sample to be large enough to use the normal distribution with a binomial, we use the
rule that:
a. p(1-p) must be negative
b. the sample size must be smaller than 30
c. any sample size will work
d. np and n(1-p) both must be greater than or equal to 5
e. the sample mean must be larger than the sample proportion.
4. When using the sample mean to estimate the population mean, the margin of error is
a. the standard deviation divided by the sample size
b. the probability that the mean will take on the value in the null hypothesis but still be wrong.
c. not really all that important (-10,000,001 points if you choose this one)
d. the largest error that would be expected in the sample mean for the given confidence.
e. only used in surveys to indicate the number of people sampled
5. The hypothesis that you wish to support is the
a. null hypothesis
b. type I hypothesis
c. 
d. confidence hypothesis
e. alternative hypothesis
6. If the null hypothesis is “You are healthy” and a medical test says that you are ill when in fact you are
healthy, then the test has committed a(n)
a. beta
b. null hypothesis
c. type III error
d. no error has resulted
e. type I error
7. If the null hypothesis is that the average grade is at least 75, then the rejection region is
a. two-sided
b. left-sided
c. right-sided
d. the null hypothesis
e. all the answers are correct
8. The standard error of the sample mean is
a.  divided by the square root of n
b. 
c. the sample mean divided by 
d. the square root of the standard deviation divided by the mean
e. a non-typical error
9. When trying to determine the probability that the sample proportion is greater than 0.23, you would
need to know
a. the pie chart
b. the level of significance of the sample proportion
c. the rejection region
d. the standard error of the sample proportion
e. the distance that the sample mean is from the sample proportion.
10. If in the past the average temperature of healthy people has been 98.6 on average and you wish to see
if this is wrong, then the null hypothesis is
a. Ho x = 98.6
b. Ho  = 98.6
c. Ho s < 98.6
d. Ho  ≠ 98.6
e. Ho  > 98.6
11. Suppose the alternative hypothesis is “the average sales of a product is above 50”, a type 2 error is
a. concluding the average sales could be 50
b. concluding that the average sales is less than 50 when in fact the average sales equals 50
c. concluding that the average sales could be 50 when in fact the average sales is above 50
d. the alternative hypothesis
e. something I wish that I studied more (Hint: wrong answer)
12. What letter represents the probability of incorrectly concluding that the null is wrong?
a.
b.
c.
d
e.
13. The distance that the sample mean is from the hypothesized value (in standard errors) is called:
a. the test statistic
b. alpha
c. the hypothesized value
d. George
e. always correct
14. 89.25% of the values of Z fall less than the value:
a. -1.01
b. 1.00
c. 1.24
d. -0.45
e. none of the above
15. Find Pr(-1.21 < Z < -0.23)
a. 0.0003
b. 0.5691
c. 1.2342
d. 0.2959
e. none of the others are correct
16. The grades on a test are normally distributed with a mean of 75 and a standard deviation of 10. A
student’s grade was on the 85th percentile. Rounding to the nearest point, what grade did the student
make?
a. 98
b. 85
c. 62
d. 14
e. none of the others are correct.
17. What would be the conclusion of a confidence interval for the mean if the sample mean is 24, the
population standard deviation is 10 and the sample size is 100? We are 95% confident that …
a. the population mean is 24 plus or minus a margin of error of 1.96
b. the sample mean is within the interval
c. the sample mean is 24.
d. the hypothesis will be rejected.
e. the population mean is 24.
18. Given a normally distributed population with mean of 55 and standard deviation of 15, what is the
probability of finding a sample mean above 57? The sample size is 25.
a. 0.9975
b. 0.7486
c. 0.2374
d. 0.1435
e. none of the others are correct
19. What would be the rejection region when trying to support the alternative hypothesis that the
population mean differs from 45? (The significance level is 0.04)
a. reject Ho if z > 2.05 or z < -2.05
b. reject H1 if Z > 1.645
c. reject Ho if x differs from 45.
d. 1.96
e. impossible to determine with this information.
20. What sample size would be needed to estimate the population average to within 0.005 inches if the
population standard deviation was 0.03 inches. Use 95% confidence.
a. 24
b. 1,234
c. 1.96
d. can not be solved
e. none of the other answers are correct
21. The average diameter of bearings being produced by a shop should be 1.5 inches in diameter. You
determine a test statistic value of 2.12. If the level of significance is 0.02, what would be your conclusion?
(Assume the population standard deviation is known.)
a. We can say the average diameter of the bearings differs from 1.5 inches.
b. We can say the average diameter of the bearings equals 2.12 inches.
c. We can not say the average diameter of the bearings differs from 1.5 inches.
d. We can not say the average diameter of the bearings differs from 0.02 inches.
e. The probability of the sample mean is 212%
22. A sample proportion is a special case of
a. a sample mean
b. a non random sample
c. a rejection region
d. a variance
e. nothing
23. You have randomly sampled the financial ratios of 25 stocks and want to know the average financial
ratio of all stocks. You would use
a. a nonrandom sample
b. a test of hypothesis
c. the probability of a population proportion
d. a test statistic
e. a confidence interval
24. In the past the cost of living in a city had a standard deviation of 5,000. You are trying to support the
hypothesis that the average cost of living exceeds 30,000. Suppose x =25,000, what can you conclude at
a 5% level of significance?
a. We can say that the average cost of living does exceed 30,000
b. We can not say that the average cost of living exceeds 30,000
c. We can say that average cost of living equals 30,000
d. We can say the sample average is 5,000
e. not enough information is given to make a conclusion
25. When calculating a 95% confidence interval for the average length of life of light bulbs, you are 100%
sure
a. statistics will give you the correct value of the population mean
b. the confidence interval is correct
c. the wind is from the north
d. the sample mean is not the population mean
e. statistics is not important (you had better NOT choose this answer)
Answers:
1. The values of the sample mean and their probabilities that result from taking random samples is called
a(n) sampling distribution
2. What is a requirement of all confidence intervals and hypothesis tests?
simple random sample
3. In order for the sample to be large enough to use the normal distribution with a binomial, we use the
rule that np and n(1-p) both must be greater than or equal to 5
4. When using the sample mean to estimate the population mean, the margin of error is the largest error
that would be expected in the sample mean for the given confidence
5. The hypothesis that you wish to support is the alternative hypothesis
6. If the null hypothesis is “You are healthy” and a medical test says that you are ill when in fact you are
healthy, then the test has committed a type I error
7. If the null hypothesis is that the average grade is at least 75, then the rejection region is left-sided. (The
alternative is that the average is less than 75.)
8. The standard error of the sample mean is  divided by the square root of n
9. When trying to determine the probability that the sample proportion is greater than 0.23, you would
need to know the standard error of the sample proportion. (The z-value is the difference between the
value 0.23 and the population proportion in number of standard errors. You then use the z in the greater
than table to find the probability.)
10. If in the past the average temperature of healthy people has been 98.6 on average and you wish to see
if this is wrong, then the null hypothesis is Ho  = 98.6 (The null hypothesis contains the status quo. It
can not be Ho x = 98.6 becausex can be found exactly and doesn’t need to be tested. Only  is
unknown here.)
11. Suppose the alternative hypothesis is “the average sales of a product is above 50”, a type 2 error is
concluding that the average sales could be 50 when in fact the average sales is above 50. (A type 2
error is not rejecting the null when you should have rejected it. Saying the null is true when actually the
alternative is true.)
12.  represents the probability of incorrectly concluding that the null is wrong. ( is the probability of a
type 1 error)
13. The distance that the sample mean is from the hypothesized value (in standard errors) is called the
test statistic. (The test statistic when  is known is ( x   ) /  x )
14. 89.25% of the values of Z fall less than the value 1.24.
15. Find Pr(-1.21 < Z < -0.23) = 0.2959. [ Pr(Z<-0.23) – Pr(Z<-1.21)= 0.4090 – 0.1131 =0.2959]
16. The grades on a test are normally distributed with a mean of 75 and a standard deviation of 10. A
student’s grade was on the 85th percentile. Rounding to the nearest point, what grade did the student
make? 85 (A percentile is concerned with the probability of being below a value. 85% of the z values fall
less than 1.04. The grade is then 1.04 standard deviations above the mean = 75 + 1.04*10 = 85.4)
17. What would be the conclusion of a confidence interval for the mean if the sample mean is 24, the
population standard deviation is 10 and the sample size is 100? We are 95% confident that the
population mean is 24 plus or minus a margin of error of 1.96.
(The standard error is  / n  10 / 100  1 . The margin of error is Z times the standard error. For
95% confidence this would be then 1.96*1. The confidence interval is then the sample mean plus or
minus the margin of error.)


18. Given a normally distributed population with mean of 55 and standard deviation of 15, what is the
probability of finding a sample mean above 57? The sample size is 25. The probability is 0.2514 (which
was none of the ones listed).
(The standard error is 15/5 = 3. The z values becomes (57-55)/3 = 0.67. The probability of finding a z
greater than 0.67 is 0.2514)
19. What would be the rejection region when trying to support the alternative hypothesis that the
population mean differs from 45? (The significance level is 0.04) reject Ho if z > 2.05 or z < -2.05
(This is a two-sided alternative so alpha is split into two parts of 0.02 each. The z values corresponding to
the two parts are -2.05 and 2.05. The rejection region is values that fall further from the mean by 2.05
standard errors either direction)
20. What sample size would be needed to estimate the population average to within 0.005 inches if the
population standard deviation was 0.03 inches. Use 95% confidence. The sample size needed is 139
(none of the answers were correct) (Using the sample formula with the margin of error is 0.005,  =
0.03 and z = 1.96 results in a value of 138.2976 which rounds up to 139)
21. The average diameter of bearings being produced by a shop should be 1.5 inches in diameter. You
determine a test statistic value of 2.12. If the level of significance is 0.02, what would be your conclusion?
We can not say the average diameter of the bearings differs from 1.5 inches.
(The status quo, the null hypothesis, is that  = 1.5. Values far above 1.5 or far below 1.5 would cause
you to reject the status quo, a two-sided rejection region. The rejection region is Reject Ho if Z > 2.33 or
Z <-2.33. Since 2.12 does not fall in the rejection region, we can not conclude that the average diameter
differs from 1.5.)
22. A sample proportion is a special case of a sample mean
23. You have randomly sampled the financial ratios of 25 stocks and want to know the average financial
ratio of all stocks. You would use a confidence interval.
24. In the past the cost of living in a city had a standard deviation of 5,000. You are trying to support the
hypothesis that the average cost of living exceeds 30,000. Suppose x =25,000, what can you conclude at
a 5% level of significance? Not enough information is given to make a conclusion since you need to
know the sample size to complete the calculation of Z.
25. When calculating a 95% confidence interval for the average length of life of light bulbs, you are 100%
sure the sample mean is not the population mean
(Has there been a day when I did not say the sample mean is in error when trying to estimate the
population mean?)