Part I: Multiple Choice (Questions 1-10) - Circle the ...

Chapter 19-22 Practice Test

Name______________________________

Part I: Multiple Choice (Questions 1-10) - Circle the answer of your choice.

1. In an opinion poll, 25% of 200 people sampled said that they were strongly opposed to having a state lottery. The standard error of the sample proportion is approximately

(A) 0.031 (B) 0.25 (C) 0.00094 (D) 6.124 (E) 0.06

A;

2. A survey was conducted at a movie theater to determine movie-goers' preference for different kinds of popcorn. The results of the survey showed that Brand A was preferred by 65 percent of the people with a margin of error of plus or minus 3 percent. What is the meaning of the statement "plus or minus 3 percent"?

(A) Three percent of the population that was surveyed will change their minds. (B) Three percent of the time the results of such a survey are not accurate. (C) Three percent of the population was surveyed. (D) The true proportion of the population who preferred Brand A popcorn could be determined if 3

percent more of the population was surveyed. (E) It would be unlikely to get the observed sample proportion of 65 percent unless the actual

percentage of people in the population of movie-goers who prefer Brand A is between 62 percent and 68 percent.

E;

3. You want to design a study to estimate the proportion of students on your campus who agree with the statement, "The student government is an effective organization for expressing the needs of students to the administration." You will use a 95% confidence interval and you would like the margin of error to be 0.05 or less. The minimum sample size required is approximately

(A) 22 (B) 1795 (C) 385 (D) 271 (E) 543

C;

4. Which of the following statements are true?

I. The sample distribution of has a mean equal to the population proportion p.

II. The sampling distribution of has a standard deviation equal to

.

III. The sampling distribution of is considered close to normal provided that

and

.

(A) I and II (B) I and III (C) II and III (D) I, II, and III (E) None of the above gives the complete set of true responses.

B; I and III are true. II is not true; the standard deviation should be

.

5. In a random sample of 300 elderly men, 65% were married, while in a similar sample of 400 elderly women, 48% were married. Determine a 99% confidence interval estimate for the difference between the percentages of elderly men and women who were married.

(A) (B) (C) (D) (E)

B;

6. a tA building inspector believes that the percentage of new construction with serious code violations may be even greater than the previously claimed 7%. She conducts a hypothesis test on 200 new homes and finds 23 with serious code violations. Is this strong evidence against the 0.07 claim?

(A) Yes, because the p-value is 0.006. (B) Yes, because the p-value is 2.5. (C) No, because the p-value is only 0.006. (D) No, because the p-value is over 2.0. (E) No, because the p-value is 0.045.

A;

;

,

7. By what factor (approximately) will the margin of error for a value for a population proportion increase if we increase the confidence level from 95% to 98%?

(A) 0.43 (B) 0.98 (C) 1.19 (D) 1.68 (E) 2.33

C;

8. Which of the following statements are true?

I. It is helpful to examine your data before deciding whether to use a one-sided or a two-sided hypothesis test.

II. If the p-value is 0.05, the probability that the null hypothesis is correct is 0.05. III. The larger the p-value, the more evidence there is against the null hypothesis.

(A) I only (B) II only (C) III only (D) II and III (E) None of the above gives the complete set of true responses.

E; all three statements are false. For I, you should make this decision before examining the data. For II, the p-value is the probability of getting a result as extreme or greater than the test statistic assuming the null hypothesis is true. For III, it should be the smaller the p-value, the more evidence there is against the null hypothesis.

9. Which of the following are correct?

I. The power of a significance test depends on an alternative value of the parameter. II. Increasing the size of the sample will increase the power of the test. III. The probability of a Type II error is equal to the significance level of the test.

(A) I and II only (B) I and III only (C) II and III only (D) I, II, and III (E) None of the above gives the complete set of true responses.

A; for III, the probability of a Type I error is equal to the significance level of the test.

10. The U.S. Department of Labor and Statistics released the current unemployment rate of 5.3% for the month in the U.S. and claims the unemployment has not changed in the last two months. However, the states statistics reveal that there is a significant reduction in the U.S. unemployment rate. Identify the Type II error in this context.

(A) The statewide report concludes that unemployment is on the decline, but in fact there is no change in unemployment.

(B) The statewide report concludes that unemployment is declining since the unemployment rate can only decrease.

(C) The statewide report shows there in no change in unemployment, but in fact the unemployment rate is decreasing.

(D) The statewide report shows there in no change in unemployment, but in fact the unemployment rate is increasing.

(E) The sample size of the statewide report was too small.

C; a Type II error occurs when we fail to reject the null and we should.

Part II ? Free Response (Questions 11-13) ? Show your work and explain your results clearly.

11. A random sample of 415 potential voters was interviewed 3 weeks before the start of a statewide campaign for governor; 223 of the 415 said they favored the new candidate over the incumbent. However, the new candidate made several unfortunate remarks one week before the election. Subsequently, a new random sample of 630 potential voters showed that 317 voters favored the new candidate.

Do these data support the conclusion that there was a decrease in voter support for the new candidate after the unfortunate remarks were made? Give appropriate statistical evidence to support your answer.

P ? The difference in the proportion of voters supporting the candidate after the remarks were made.

H ?

,

,

A ? The two samples are independent SRS's from the population of potential voters.

The population is greater than 10 times each of the sample sizes

and

.

The number of successes and failures are all greater than 10 (223,317, 192, 313).

N ? Two Proportion Z-Test

T ?

, (1.082 using the test on the calculator)

O ?

, (.140 using the test on the calculator)

M ? Since the p-value is large, we fail to reject the null hypothesis.

S ? The difference in the proportion of voters supporting the candidate after the remarks were made is not statistically significant. We do not have evidence the remarks resulted in a decrease of voter support.

12. A large university provides enough housing for 10 percent of its graduate students to live on campus. The university's housing office thinks that the percent of graduate students looking on campus may be more than 10 percent. The housing office decides to survey a random sample of graduate students, and 62 of the 481 respondents say that they are looking for housing on campus.

(a) On the basis of the survey data, would you recommend that the housing office consider increasing the amount of housing on campus available to graduate students? Give appropriate statistical evidence to support your recommendation.

P ? The proportion of graduate students seeking housing.

H ?

A ? The sample is an SRS from the population of all graduate students.

The population is greater than 10 times the sample size

.

,

N ? One Proportion Z-Test

T ?

, (2.113 using the test on the calculator)

O ?

, (.017 using the test on the calculator)

M ? Since the p-value is small, we reject the null hypothesis. S ? We have evidence the proportion of graduate students seeking housing is greater than 10%.

(b) In addition to the 481 graduate students who responded to the survey, there were 19 who did not respond. If these 19 had responded, is it possible that your recommendation would have changed? Explain.

Perhaps. If the 19 students did not need housing then

. This would result in a p-value of

.037. If they did need housing

resulting in a p-value of less than .001.

13. Respondents who had a tree during the holiday season were asked whether the tree was natural or artificial. Respondents were also asked if they lived in an urban area or in a rural area. Of the 421 households displaying a Christmas tree, 160 lived in rural areas and 261 were urban residents. The tree growers want to know if there is a difference in preference for natural trees versus artificial trees between urban and rural households. The tree growers found that 40% of the rural households prefer a natural tree and 34.1% of the urban households prefer a natural tree.

(a) Create a 95% confidence interval for the difference between rural and urban households.

P ? The difference in the proportion of rural residents and urban residents that prefer a natural tree.

A ? The two samples are independent SRS's from the populations of all rural and urban residents.

The population is greater than 10 times each of the sample sizes

and

.

,

N ? Two Proportion 95% Z-Interval

I ?

C ? We are 95% confident that the difference in the proportion of rural residents and urban residents that prefer a natural tree is between -.036 and .154.

(b) Interpret the meaning of the level of 95% confidence.

If this method were repeated many times, approximately 95% of the resulting intervals would capture the true population difference in the proportion of rural residents and urban residents that prefer a natural tree.

(c) Does the interval provide evidence that a difference exists in the preferences of rural and urban residents?

No; since zero is contained in the interval, we do not have evidence the difference in the proportion of rural residents and urban residents that prefer a natural tree is statistically significant.

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