Statistical Analysis: Confidence Intervals and Hypothesis Tests, Assignments of Statistics

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Stat 250.3 November 10, 2003

Activity 7: Confidence Intervals and Hypothesis Tests Situation 1: A sociologist wants to know how much more money on average a husband makes than his wife. The sociologist records the salaries for 40 random couples (assume both husband and wife are employed). A) What type of data is this? B) Suppose that the sample mean salary for husbands was $52,000 and the sample mean salary for women was $41,000. Differences are taken for each pair and the husband’s salary is $11,000 more on average with a standard deviation of the differences equal to $8000. Construct a 95% confidence interval for the mean difference in salaries between husbands and wives. Parameter of Interest: Statistic of Interest: Conditions: Confidence interval calculations: Interpretation of the CI: C) Test the hypothesis that on average the salaries of the husbands are higher than the ones of their wives. Situation 2: A scientist wants to know how effective a new drug is at lowering blood pressure. He randomly assigns 70 patients to receive either the blood pressure lowering drug, or a placebo (half get each). The average decrease in blood pressure for the drug group is 8 with a standard deviation of 10. The average decrease for placebo was 2 with a standard deviation of 4. A) Construct an appropriate 99% confidence interval for the difference in the mean decrease in blood pressure between the drug and placebo. Parameter of Interest: Statistic of Interest: Conditions: Confidence interval calculations: B) Test the hypothesis that the drug is effective. (i.e. works better than the placebo) at alpha=0.01 significance level.

Stat 250.3 November 10, 2003

Situation 3: 12.7 From the Text A study was done by randomly assigning 200 volunteers with sore throats to either drink a cup of herbal tea or use a sore throat lozenge to ease their pain. The percent reporting relief for the two methods were compared. What are the research question, the population parameter, and the sample statistic for this study? Situation 4: A random sample of students was surveyed on whether they smoked pot, and whether they ever tried a “harder” drug (cocaine, heroin, etc.) The summary statistics for the two variables were as follows: X = Number who Used a Harder Drug Test and CI for Two Proportions Sample X N Sample p Pot 34 140 0. No Pot 40 248 0. Estimate for p(1) - p(2): 0. 95% lower bound for p(1) - p(2): 0. Test for p(1) - p(2) = 0 (vs > 0): Z = 1.89 P-Value = 0. A) Create a 95% for the difference in proportion of students that smoked pot and that did not smoked pot that tried a “harder” drug. B) Is there enough evidence to conclude that a higher proportion of students who smoked pot than students who did not try pot have tried a “harder” drug?