Understanding CI and HT: Analyzing Two-Sample Data and Claims

CI and HT Two-Sample 1. A study was done to determine whether there is a relationship between snoring and the risk of heart disease. Among 1105 snorers (Group1) in the study 85 had heart disease while only 24 of 1379 non-snorers (Group2) had heart disease. Construct a 95% CI to estimate the difference (p 1 - p 2 ) and interpret the CI. 0.046 to 0.081 2. A Gallup poll conducted in 2020 asked the question: Do you feel that laws covering the sale of firearms should be made stricter? Of the n = 493 men who responded, 273 said Yes. Of the 538 women who responded, 352 said Yes. Assuming that these respondents represent random samples of U.S. men and women, is there sufficient evidence to conclude that a higher proportion of women than men think that these laws should be stricter? Use a significance level of 0.05. The critical value of z at a 0.05 significance level for a two-tailed test is ±1.96. Since the calculated z-value of 5.25 is greater than 1.96, we reject the null hypothesis that the proportion of women who think that laws covering the sale of firearms should be made stricter is equal to the proportion of men who think so. Therefore, we have sufficient evidence to conclude that a higher proportion of women than men think that these laws should be stricter.

3. Professor Andy Neill measured the time (in seconds) required to catch a falling yard stick for 12 randomly selected students’ dominant hand and nondominant hand. Professor Neill claims that the reaction time in an individual’s dominant hand is less than the reaction time in their nondominant hand. Test the claim at the α = 0.05 level of significance. Here is the data: Student Dominant Hand, x 1 Nondominan t hand, x 2 Difference : x 1 -x 2 1 0.177 0.179 2 0.210 0.202 3 0.189 0.184 4 0.198 0.215 5 0.194 0.193 6 0.160 0.194 7 0.163 0.160 8 0.166 0.209 9 0.152 0.164 10 0.190 0.210 11 0.172 0.197 12 0.186 0.208 T=-2.86

There is sufficient evidence to support Professor Neils's claim that the reaction time in an individual's dominant hand is less than the reaction time in their non-dominant hand. 4. Suppose that the Smith CPA firm in Chicago claims that its clients receive larger tax refunds, on average, than clients of its competitor, Jones and Company CPA, located on the other side of Chicago. To test the claim, 15 clients from the Smith firm are randomly selected and found to have a mean tax refund of $942 with a standard deviation of $103. At Jones and Company, a random sample of 18 clients were surveyed and found to have a mean refund of $898 with a standard deviation of $95. Test the claim of the Smith firm at the 0.05 level of significance. Assume that both of the population distributions are approximately normal. Use the Unpooled method. Null hypothesis: H0: μ1 = μ2 (There is no difference in the mean tax refunds between clients of the Smith CPA firm and clients of Jones and Company CPA.) Alternative hypothesis: Ha: μ1 ≠ μ2 (There is a difference in the mean tax refunds between clients of the Smith CPA firm and clients of Jones and Company CPA.) b) Conditions for the normal distribution: Met (sample sizes > 30 and no reason to believe data is not normally distributed). c) P-value: 0.0782 d) Conclusion: Fail to reject null hypothesis (not enough evidence to conclude a difference in mean tax refunds). e) Confidence interval: (-32.48, 97.48) f) Interpretation of confidence interval: 95% confidence that the true difference in mean tax refunds lies between -$32.48 and $97.48. Since the interval includes zero, this aligns with the hypothesis test conclusion of no difference in mean tax refunds.

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5. A researcher wants to know who reads more, Millenials or GenXers. She surveys 28 Millenials and finds that they read a mean of 2.5 books per month with a standard deviation of 0.9 books. For the 25 members of Generation X that she surveys, she finds that they read a mean of 2.1 books per month with a standard deviation of 0.8 books. Using the Unpooled method, construct a 95% CI for the true difference between the mean number of books read each month by these two generations and interpret your CI -0.0691,0.8691 We are 95% confident that true difference between the mean number of books read each month by these two generations is between −0.0691 and 0.8691

9_CI and HT_Two-Sample

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