10. Hypothesis Testing for Two Samples

Hypotheses and Conclusions Refer to the hypothesis test described in Exercise 1.

b. If the P-value for the test is reported as “less than 0.001,” what should we conclude about the original claim?

Efficacy of e-Cigs Do electronic cigarettes assist in helping individuals quit smoking? Researchers found 300 current smokers to volunteer for a study in which each was randomly assigned to one of three treatment groups. Group 1 received an electronic cigarette (e-cig) in which each cartridge contained 7.2 mg of nicotine, Group 2 received an e-cig that contained 5.4 mg of nicotine, and Group 3 received an e-cig that contained no nicotine. The subjects did not know which group they were assigned. During the course of the 52-week intervention, subjects dropped out of the study. At the end of the study 65 subjects remained in Group 1, 63 in Group 2, and 55 in Group 3. After 52 weeks, it was determined via questionnaire whether the subject quit smoking entirely. Results of the study are presented in the following table.

g. Write a conclusion for this hypothesis test.

In Exercises 1–10, based on the nature of the given data, do the following:

a. Pose a key question that is relevant to the given data.

b. Identify a procedure or tool from this chapter or the preceding chapters to address the key question from part (a).

c. Analyze the data and state a conclusion.

Video Games In a survey of subjects aged 18–29, subjects were asked if they play video games often or sometimes. Among 1017 males, 72% answered “yes.” Among 984 females, 49% answered “yes” (based on data from a Pew Research Center survey).

Smoking Cessation Programs

a. Construct the confidence interval that could be used to test the claim in Exercise 5. What feature of the confidence interval leads to the same conclusion from Exercise 5?

Smoking Cessation Programs

b. Does the difference between the success rate of the sustained care program and the standard care program appear to have practical significance?

Practical versus Statistical Significance In clinical trials for treatment of a skin disorder, 642 of 2105 patients receiving the current standard treatment were cured of the disorder and 697 of 2115 patients receiving a new proposed treatment were cured of the disorder.

b. Do you think that the difference in success rates is practically significant? What factors might influence your decision?

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.

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.

P-VALUE The test statistic of z = 2.14 is obtained when using the data from Exercise 1 and testing the claim that patients treated with dexamethasone and patients given a placebo have the same rate of complete resolution.

a. Find the P-value for the test.

In Exercises 5–8, use (a) randomization and (b) bootstrapping for the indicated exercise from Section 9-1. Compare the results to those obtained in the original exercise.

Exercise 7 in Section 9-1 “Buttered Toast Drop”

In Exercises 5–8, use (a) randomization and (b) bootstrapping for the indicated exercise from Section 9-1. Compare the results to those obtained in the original exercise.

Exercise 8 in Section 9-1 “Tennis Challenges”

In Exercises 5–8, use (a) randomization and (b) bootstrapping for the indicated exercise from Section 9-1. Compare the results to those obtained in the original exercise.

Exercise 9 in Section 9-1 “Cell Phones and Handedness”