9. Hypothesis Testing for One Sample

Test Values p_cap1, p_cap2. Find the values of and the pooled proportion p_bar obtained when testing the claim given in Exercise 1.

Identifying Hypotheses In a randomized clinical trial of adults with an acute sore throat, 288 were treated with the drug dexamethasone and 102 of them experienced complete resolution; 277 were treated with a placebo and 75 of them experienced complete resolution (based on data from “Effect of Oral Dexamethasone Without Immediate Antibiotics vs Placebo on Acute Sore Throat in Adults,” by Hayward et al., Journal of the American Medical Association). Identify the null and alternative hypotheses corresponding to the claim that patients treated with dexamethasone and patients given a placebo have the same rate of complete resolution.

Randomization: Testing a Claim About a Mean

In Exercises 9–12, use the randomization procedure for the indicated exercise.

Section 8-3, Exercise 23 “Cell Phone Radiation”

Perception and Reality In a presidential election, 308 out of 611 voters surveyed said that they voted for the candidate who won (based on data from ICR Survey Research Group). Use a 0.05 significance level to test the claim that among all voters, the percentage who believe that they voted for the winning candidate is equal to 43%, which is the actual percentage of votes for the winning candidate. What does the result suggest about voter perceptions?

Test for Normality For the hypothesis test described in Exercise 2, the sample sizes are n1 = 2208 and n2 = 1986 When using the F test with these data, is it correct to reason that there is no need to check for normality because both samples have sizes that are greater than 30?

Right-Tailed, Left-Tailed, Two-Tailed Is the hypothesis test described in Exercise 1 right-tailed, left-tailed, or two-tailed? Explain your choice.

Ghosts The following table summarizes results from a Pew Research Center survey in which subjects were asked whether they had seen or been in the presence of a ghost. Use a 0.01 significance level to test the claim that gender is independent of response. Does the conclusion change if the significance level is changed to 0.05?

Accuracy of Fingerprint Identifications An experiment was conducted to compare the accuracy of fingerprint experts to the accuracy of novices (based on data from “Identifying Fingerprint Expertise,” by Tangen, Thompson, and McCarthy, Psychological Science, Vol. 22, No. 8). The data in the table are based on trials in which the evaluators were given matching fingerprints. Use a 0.05 significance level to determine whether correct identification is independent of whether the evaluator is an expert or a novice.

Gender and Eye Color The following table describes the distribution of eye colors reported by male and female statistics students (based on data from “Does Eye Color Depend on Gender? It Might Depend on Who or How You Ask,” by Froelich and Stephenson, Journal of Statistics Education, Vol. 21, No. 2). Is there sufficient evidence to warrant rejection of the belief that gender and eye color are independent traits? Use a 0.01 significance level.

Clinical Trial of Echinacea In a clinical trial of the effectiveness of echinacea for preventing colds, the results in the table below were obtained (based on data from “An Evaluation of Echinacea Angustifolia in Experimental Rhinovirus Infections,” by Turner et al., New England Journal of Medicine, Vol. 353, No. 4). Use a 0.05 significance level to test the claim that getting a cold is independent of the treatment group. What do the results suggest about the effectiveness of echinacea as a prevention against colds?

Equivalent Tests A x^2 test involving a 2 x 2 table is equivalent to the test for the difference between two proportions, as described in Section 9-1. Using Table 11-1 from the Chapter Problem, verify that the x^2 test statistic and the z test statistic (found from the test of equality of two proportions) are related as follows: z^2 = x^2 Also show that the critical values have that same relationship.

Robust What does it mean when we say that the F test described in this section is not robust against departures from normality?

Exercises 1–5 refer to the sample data in the following table, which summarizes the frequencies of 500 digits randomly generated by Statdisk. Assume that we want to use a 0.05 significance level to test the claim that Statdisk generates the digits in a way that they are equally likely.

What are the null and alternative hypotheses corresponding to the stated claim?

Exercises 1–5 refer to the sample data in the following table, which summarizes the frequencies of 500 digits randomly generated by Statdisk. Assume that we want to use a 0.05 significance level to test the claim that Statdisk generates the digits in a way that they are equally likely.

Is the hypothesis test left-tailed, right-tailed, or two-tailed?

Questions 6–10 refer to the sample data in the following table, which describes the fate of the passengers and crew aboard the Titanic when it sank on April 15, 1912. Assume that the data are a sample from a large population and we want to use a 0.05 significance level to test the claim that surviving is independent of whether the person is a man, woman, boy, or girl.

Identify the null and alternative hypotheses corresponding to the stated claim.