Are You Suprised ? s2

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

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.

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

4. Which of the following statements are true? I. The sample distribution of pˆ has a mean equal to the population proportion p. II. The sampling distribution of pˆ has a standard deviation equal to np 1 p .   III. The sampling distribution of pˆ is considered close to normal provided that np  10 and n(1- p) 10 .

(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. 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) 17%  0.36% (B) 17%  9.6% (C) 55%  6.7% (D) 56%  6.7% (E) 56.5%  9.6%

6. A 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.

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

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.

9. Which of the following are correct? I. The power of a significance test depends on the alternative value of the parameter. II. Type I and Type II errors only make sense when a significance level has been chosen in advance. 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. 10. Which of the following will increase the value of the power in a statistical test of hypotheses?

I. Increase the significance level. II. Increase the sample size. III. Consider computing the power for a value of the alternative that is farther from the value of the parameter of interest under the null hypothesis.

(A) I (B) II (C) III (D) I and II (E) I, II, and III

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 state-wide 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.

12. Do more than 50% of Americans feel that they get enough sleep? According to Gallup’s December 2004 Lifestyle poll, 55% of U.S. adults said that they get enough sleep. The poll was based on a random sample of 1003 U.S. adults. Test an appropriate hypothesis and state your conclusion in the context of the problem. 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.

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

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