CHAPTER 8 REVIEW QUIZ (11 POINTS)

Use the following to answer questions 1-2:

A researcher is studying the failure rate of restaurants. She selects a random sample of 200 restaurants in large cities that opened within the last year. Following up on these restaurants, she finds that 80 had failed within five years.

1. / A 99% confidence interval for the proportion of restaurants that fail within five years is
A) / 0.402 ± 0.035.
B) / 0.402± 0.044.
C) / 0.402 ± 0.057.
D) / 0.402 ± 0.089.

Ans: D

2. / To determine if opening a restaurant in a large city increases the chance of failure compared to opening a restaurant in a suburban or rural area we should
A) / test the hypotheses H0: p = 0.50, Ha: p ¹ 0.50.
B) / test the hypotheses H0: p = 0.50, Ha: p > 0.50.
C) / test the hypotheses H0: p = 0.40, Ha: p > 0.40.
D) / do none of the above.

Ans: D

Use the following to answer questions 3-4:

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

H0: p = 0.10, Ha: p < 0.10

using the large sample test for a population proportion. To do so, she selects an SRS of 150 potatoes from the over 3000 potatoes on the truck. Suppose that only six of the potatoes sampled are found to have major defects.

3. / The P-value of her test is
A) / less than 0.0002.
B) / 0.0010.
C) / 0.0071.
D) / 0.0142.

Ans: C

4. / 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 np0 and n(1 – p0) are 10 or more, where p0 is the proportion with major defects, if the null hypothesis is true.
D) / There appear to be no violations.

Ans: D

5. / A newspaper conducted a statewide survey concerning the 2000 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
H0: p = 0.50, Ha: p > 0.50.
The P-value of your test is
A) / 0.4920.
B) / 0.0330.
C) / 0.0104.
D) / less than 0.0002.

Ans: C

Use the following to answer questions 6-8:

A recent book noted that only 20% of investment managers outperform the standard indexes, such as the Dow Jones Industrial Average or the NASDAQ, over a five-year period. A sample of 200 investment managers that had graduated from one of the top ten business programs in the country were followed over a five-year period. Fifty of these outperformed the Dow Jones Industrial Average. Let p represent the probability that a random investment manager who graduated from one of the top ten business programs will outperform the Dow Jones over a five-year period.

6. / Based on the results of the sample, a 95% confidence interval for p is
A) / 0.25 ± 0.060.
B) / 0.25 ± 0.055.
C) / 0.25 ± 0.050.
D) / We can assert that p = 0.20 with 100% confidence, because only 20% of investment managers outperform the standard indexes.

Ans: A

7. / Suppose you wished to see if there is evidence that graduates of one of the top business programs perform better than other investment managers. To do this, you test the hypotheses
H0: p = 0.20, Ha: p > 0.20.
The P-value of your test is
A) / between .10 and .05.
B) / between .05 and .01.
C) / between .01 and .001.
D) / below .001.

Ans: B

8. / How large a sample n would you need to estimate p with margin of error 0.01 with 95% confidence? Use the guess p = 0.20 as the value for p.
A) / n = 4326
B) / n = 6143
C) / n = 7199
D) / n = 9600

Ans: B

Use the following to answer questions 9-10:

After the football team once again lost a game to the college's arch rival, the 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.

9. / A 95% confidence interval for p is
A) / 0.63 ± 0.047.
B) / 0.63 ± 0.078.
C) / 0.63 ± 0.093.
D) / 0.63 ± 0.128.

Ans: C

10. / Suppose you wished to see if the majority of alumni are in favor of firing the coach. To do this you test the hypotheses
H0: p = 0.50, Ha: p > 0.50.
The P-value of your test is
A) / between .10 and .05.
B) / between .05 and .01.
C) / between .01 and .001.
D) / below .001.

Ans: C

11. / A radio talk show host with a large audience is interested in the proportion p of adults in his listening area who 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) / A third choice of no opinion needed to be included.
D) / There appear to be no violations.

Ans: A