Additional Practice 1. The Pew Research Center found in a recent survey that 61% of teenage girls surveyed use Instagram, compared to 44% of the boys. The report on this survey states that the difference is statistically significant. Explain what they meant by that. 2. The Centers for Disease Control and Prevention reported from a survey of randomly selected U.S. seniors age 65 of older that 41 1 of 1012 men and 535 of 1062 women suffered from some form of arthritis. a. Are the conditions for inference satisfied? b. Do these data indicate that a higher proportion of women of age 65 and older are affected by arthritis than men in the same age group? Carry out a significance test to answer the question. 1023. In 1997 a random sample of 200 low income families was taken and it was found that 43 of them did not have health insurance. In 2003 a similar survey of 270 families was taken and 42 did not to have health insurance. Follow the steps below to determine whether there is statistically significant evidence from these samples that the proportion of low income families without insurance changed over that time. Use a 10% signicance level. a. State the null and alternative hypotheses. Be careful to base the alternative on the wording of the question. b. Are the conditions satisfied for inference? c. State your conclusion in context using the results from the condence interval and the z-test shown in the computer output below: Test and CI for Two Proportions Sample X N Sample P 1997 43 200 0.2150 2003 42 270 0.1555 Difference = p(1997) p(2003) Estimate for difference: 0.3706 90% CI: (-0.0006, 0.1194) Test for difference = 0 (vs # 0): z = 1.655 p-value: 0.0978 103 4. Here is a two-way table comparing the effectiveness of two drugs, Lithium and Imipramine, in preventing a recurrence of depression among patients who were hospitalized with depression: Recurrence No Recurrence Imipramine 8 21 Lithium 1 8 9 You may have previously used exploratory data analysis (conditional distributions and a segmented bar graph) to investigate the relationship between drug and the frequency of recurrence. Now use a test of signicance to determine whether the apparent advantage of Imipramine shown in the data above could simply be due to chance. Follow the steps below: a. Find the sample proportions [3 Lithium and 13 [mm/amine that had a recurrence. Then nd the pooled proportion. b. State the null and alternative hypotheses, check the conditions for inference, and then compute the test statistic and pvalue for the data. c. Does the data give convincing evidence that Imipramine is better than Lithium at preventing a recurrence of depression? 104