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30 Multiple Choice Questions on Statistical Methods with Answer Key | STA 2023, Exams of Data Analysis & Statistical Methods

Valencia CollegeData Analysis & Statistical Methods

Material Type: Exam; Class: Statistical Methods; Subject: STA: Statistics; University: Valencia Community College; Term: Unknown 1998;

Typology: Exams

Pre 2010

Uploaded on 08/04/2009

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STA 2023 Test #3 Practice Multiple Choice
1. A newspaper conducted a statewide survey concerning the 1998 race for state senator. The
newspaper took a random sample (assume it is an SRS) of 1200 registered voters and found that
620 would vote for the Republican candidate. Let p represent the proportion of registered voters
in the state that would vote for the Republican candidate. A 90% confidence interval for p is
A) 0.517 ± 0.014.
B) 0.517 ± 0.024.
C) 0.517 ± 0.028.
D) 0.517 ± 0.249.
2. After once again losing a football game to the arch rival, a college's alumni association conducted
a survey to see if alumni were in favor of firing the coach. An SRS of 100 alumni from the
population of all living alumni was taken. 64 of the alumni in the sample were in favor of firing
the coach. Let p represent the proportion of all living alumni who favor firing the coach. A 95%
confidence interval for p is
A) 0.64 ± 0.079.
B) 0.64 ± 0.094.
C) 0.64 ± 0.124.
D) 0.64 ± 0.360.
3. In formulating hypotheses for a statistical test of significance, the null hypothesis is often
A) a statement of "no effect" or "no difference."
B) the probability of observing the data you actually obtained.
C) a statement that the data are all 0.
D) 0.05.
4. In their advertisements, the marketers of a new diet program would like to claim that their
methods result in a mean weight loss of more than 10 pounds in two weeks. In order to determine
if this is a valid claim, they hire an independent testing agency which then selects 25 people to be
placed on this diet. The agency should be testing the null hypothesis
10:
0
=
µ
H
and the
alternative hypothesis
A)
10: <
µ
a
H
.
B)
10: >
µ
a
H
.
C)
10: ≠
µ
a
H
.
D)
n
H
a
σ
µ
±≠ 10:
.
5. A researcher wishes to determine if the majority of American adults over the age of 65 plan to
vote Republican in the next presidential election. Let
p
represent the proportion of the
population of all American adults over the age of 65 who plan to vote Republican in the next
presidential election. In terms of
p
, the researcher should test which of the following null and
alternative hypotheses.
A)
5.0:
0
=
pH
vs.
5.0: >
pH
a
.
B)
5.0:
0
=
pH
vs.
5.0: ≠
pH
a
.
C)
5.0:
0
=
pH
vs.
5.0: <
pH
a
.
D)
5.0:
0
=
pH
vs.
03.05.0: ±=
pH
a
, since 0.03 is the margin of error for
most polls.
pf3
pf4
pf5
pf8

Partial preview of the text

Download 30 Multiple Choice Questions on Statistical Methods with Answer Key | STA 2023 and more Exams Data Analysis & Statistical Methods in PDF only on Docsity!

STA 2023 Test #3 Practice Multiple Choice

  1. A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a random sample (assume it is an SRS) of 1200 registered voters and found that 620 would vote for the Republican candidate. Let p represent the proportion of registered voters in the state that would vote for the Republican candidate. A 90% confidence interval for p is A) 0.517 ± 0.014. B) 0.517 ± 0.024. C) 0.517 ± 0.028. D) 0.517 ± 0.249.
  2. After once again losing a football game to the arch rival, a college's alumni association conducted a survey to see if alumni were in favor of firing the coach. An SRS of 100 alumni from the population of all living alumni was taken. 64 of the alumni in the sample were in favor of firing the coach. Let p represent the proportion of all living alumni who favor firing the coach. A 95% confidence interval for p is A) 0.64 ± 0.079. B) 0.64 ± 0.094. C) 0.64 ± 0.124. D) 0.64 ± 0.360.
  3. In formulating hypotheses for a statistical test of significance, the null hypothesis is often A) a statement of "no effect" or "no difference." B) the probability of observing the data you actually obtained. C) a statement that the data are all 0. D) 0.05.
  4. In their advertisements, the marketers of a new diet program would like to claim that their methods result in a mean weight loss of more than 10 pounds in two weeks. In order to determine if this is a valid claim, they hire an independent testing agency which then selects 25 people to be

placed on this diet. The agency should be testing the null hypothesis H 0 : μ= 10 and the

alternative hypothesis

A) H a : μ< 10.

B) H a : μ> 10.

C) H a : μ≠ 10.

D)

n

H a

σ

  1. A researcher wishes to determine if the majority of American adults over the age of 65 plan to

vote Republican in the next presidential election. Let p represent the proportion of the

population of all American adults over the age of 65 who plan to vote Republican in the next

presidential election. In terms of p , the researcher should test which of the following null and

alternative hypotheses.

A) H 0 : p = 0. 5 vs. H a : p > 0. 5.

B) H 0 : p = 0. 5 vs. H a : p ≠ 0. 5.

C) H 0 : p = 0. 5 vs. H a : p < 0. 5.

D) H 0 : p = 0. 5 vs. H a : p = 0. 5 ± 0. 03 , since 0.03 is the margin of error for

most polls.

6. The mean area μ of the several thousand apartments in a new development is advertised to be

1250 square feet. A tenant group thinks that the apartments are smaller than advertised. They hire an engineer to measure a sample of apartments to test their suspicion. The appropriate null and

alternative hypotheses, H 0 and H a , for μ are

A) H 0 : μ= 1250 and H a : μ≠ 1250.

B) H 0 : μ= 1250 and H a : μ< 1250.

C) H 0 : μ= 1250 and H a : μ> 1250.

D) cannot be specified without knowing the size of the sample used by the engineer.

  1. The P-value of a test of a null hypothesis is A) the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed. B) the probability, assuming the null hypothesis is false, that the test statistic will take a value at least as extreme as that actually observed. C) the probability that the null hypothesis is true. D) the probability that the null hypothesis is false.
  2. In testing hypotheses, which of the following would be strong evidence against the null hypothesis? A) using a small level of significance. B) using a large level of significance. C) obtaining data with a small P-value. D) obtaining data with a large P-value.

9. In a statistical test of hypotheses, we say the data are statistically significant at level α if

A) α = 0.05.

B) α is small.

C) the P-value is less than α.

D) the P-value is larger than α.

  1. The weights (in pounds) of three adult males are 160, 215, and 195. The standard error of the mean of these three weights is A) 63.33. B) 190.00. C) 16.07. D) 13.12.

11. The heights (in inches) of males in the U.S. are believed to be normally distributed with mean μ.

The average height of a random sample of 25 American adult males is found to be x = 69.

inches and the standard deviation of the 25 heights is found to be S x = 4.15. The standard error

of x is

A) 0.17.

B) 0.69.

C) 0.83.

D) 2.04.

  1. An SRS of 100 postal employees found that the average time these employees had worked for the

postal service was x = 7 years with standard deviation S x = 2 years. Assume the distribution of

the time the population of employees have worked for the postal service is approximately normal

with mean μ. Are these data evidence that μ has changed from the value of 7.5 years of 20

years ago? To determine this we test the hypotheses

H 0 : μ= 7. 5

Ha : μ≠ 7. 5

using the one-sample t test. Suppose we are not sure if the population distribution is normal. In

which of the following circumstances would use of the t procedure as above yield misleading

results? A) A histogram of the data shows some skewness. B) A stem plot of the data has a small outlier. C) The sample standard deviation is large. D) None of the above.

  1. We wish to see if the dial indicating the oven temperature for a certain model oven is properly calibrated. Four ovens of this model are selected at random. The dial on each is set to 300° F and after one hour the actual temperature of each is measured. The temperatures measured are 305°, 310 °, 300°, and 305°. Assuming that the actual temperatures for this model when the dial is set to

300 ° are normally distributed with mean μ , we test whether the dial is properly calibrated by

testing the hypotheses

H 0 : μ= 300

H a : μ≠ 300.

Based on the data, the value of the one-sample t statistic is

A) 5.

B) 4.90.

C) 2.45.

D) 1.23.

Use the following to answer questions #17 and #18:

Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. Net weights actually vary

slightly from bag to bag and are normally distributed with mean μ. A representative of a consumer

advocate group wishes to see if there is any evidence that the mean net weight is less than advertised and so intends to test the hypotheses

H 0 : μ= 14

H a : μ< 14.

To do this, he selects 16 bags of this brand at random and determines the net weight of each. He finds the

sample mean to be x = 13.82 and the sample standard deviation to be S x = 0.24.

  1. Based on the above data, we would conclude

A) we would reject H 0 at significance level 0.10 but not at 0.05.

B) we would reject H 0 at significance level 0.05 but not at 0.025.

C) we would reject H 0 at significance level 0.025 but not at 0.01.

D) we would reject H 0 at significance level 0.01.

  1. Referring to the above data, suppose we were not sure if the distribution of net weights was

normal. In which of the following circumstances would we not be safe using a t procedure in this

problem? A) The mean and median of the data are nearly equal. B) A histogram of the data shows moderate skewness. C) A stem plot of the data has a large outlier. D) The sample standard deviation is large.

19. You are thinking of using a t -procedure to test hypotheses about the mean of a population using a

significance level of 0.05. You suspect the distribution of the population is not normal and may be moderately skewed. Which of the following statements is correct?

A) You should not use the t -procedure since the population does not have a normal

distribution.

B) You may use the t -procedure provided your sample size is large—say, at least 50.

C) You may use the t -procedure, but you should probably only claim the significance level

is 0.10.

D) You may not use the t -procedure. t -procedures are robust to nonnormality for

confidence intervals but not for tests of hypotheses.

20. To estimate μ , the mean salary of full professors at American colleges and universities, you

obtain the salaries of a random sample of 400 full professors. The sample mean is x = $

and the sample standard deviation is S x = $4400. A 99% confidence interval for μ is

A) 73220 ± 11440.

B) 73220 ± 572.

C) 73220 ± 431.

D) 73220 ± 28.6.

25. An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment

with major defects prior to using the potatoes to make potato chips. Unless there is clear evidence that this proportion is less than 0.10 she will reject the shipment. To reach a decision she will test the hypotheses

H 0 : p = 0. 10

H a : p < 0. 10

using the large sample test for a population proportion. To do so, she selects an SRS of 50 potatoes from the more than 2000 potatoes on the truck. Suppose that only 2 of the potatoes sampled are found to have major defects. The P-value of her test is A) 0.4207. B) 0.0793. C) 0.0154. D) less than 0.0002.

26. An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment

with major defects prior to using the potatoes to make potato chips. Unless there is clear evidence that this proportion is less than 0.10 she will reject the shipment. To reach a decision she will test the hypotheses

H 0 : p = 0. 10

H a : p < 0. 10

using the large sample test for a population proportion. To do so, she selects an SRS of 50 potatoes from the more than 2000 potatoes on the truck. Suppose that only 2 of the potatoes sampled are found to have major defects. Which of the following assumptions for inference about a proportion using a hypothesis test are violated? A) The data are an SRS from the population of interest. B) The population is at least 10 times as large as the sample.

C) n is so large that both np 0 and n ( 1 − p 0 )are 10 or more, where p 0 is the proportion

with major defects if the null hypothesis is true. D) There appear to be no violations.

  1. A newspaper conducted a statewide survey concerning the 1998 race for governor. The newspaper took a random sample (assume it is an SRS) of 1200 registered voters and found that 640 would vote for the Democratic candidate. Is this evidence that a clear majority of the population would vote for the Democratic candidate? To answer this, test the hypotheses

H 0 : p = 0. 50

H a : p > 0. 50.

The P-value of your test is A) 0.4920. B) 0.0330. C) 0.0104. D) less than 0.0002.

  1. A sociologist is studying the effect of having children within the first two years of marriage on the divorce rate. Using hospital birth records, she selects a random sample of 200 couples who had a child within the first two years of marriage. Following up on these couples, she finds that 80 couples are divorced within five years. A 90% confidence interval for the proportion of couples who had a child within the first two years of marriage and are divorced within five years is A) 0.40 ± 0.035. B) 0.40 ± 0.044. C) 0.40 ± 0.057. D) 0.40 ± 0.068.
  2. A sociologist is studying the effect of having children within the first two years of marriage on the divorce rate. Using hospital birth records, she selects a random sample of 200 couples who had a child within the first two years of marriage. Following up on these couples, she finds that 80 couples are divorced within five years. To determine if having children within the first two years of marriage increases the divorce rate over an established 30 percent for married couples in general, we should

A) test the hypotheses H 0 : p = 0. 50 , H a : p ≠ 0. 50.

B) test the hypotheses H 0 : p = 0. 50 , H a : p > 0. 50.

C) test the hypotheses H 0 : p = 0. 40 , H a : p > 0. 40.

D) None of the above.

  1. A radio talk show host with a large audience is interested in the proportion p of adults in his listening area that think the drinking age should be lowered to 18. To find this out he poses the following question to his listeners. "Do you think that the drinking age should be reduced to 18 in light of the fact that 18 year olds are eligible for military service?" He asks listeners to phone in and vote "yes" if they agree the drinking age should be lowered and "no" if not. Of the 100 people who phoned in 70 answered "yes." Which of the following assumptions for inference about a proportion using a confidence interval are violated? A) The data are an SRS from the population of interest. B) The population is at least 10 times as large as the sample.

C) n is so large that both the count of successes np ˆ^ and the count of failures

n (1 - p ˆ^ ) are 10 or more.

D) There appear to be no violations.

ANSWER KEY:

1. B

2. B

3. A

4. B

5. A

6. B

7. A

8. C

9. C

10. C

11. C

12. A

13. C

14. C

15. D

16. C

17. D

18. C

19. B

20. B

21. C

22. B

23. A

24. B

25. B

26. C

27. C

28. C

29. D

30. A