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## Week 2 Practice with Data

1. Table 2.15 (Cholesterol.xlsx) from Rosner shows cholesterol levels (mg/dL) before and after a particular diet.  Use this dataset to answer the following questions. For each question, provide both Stata code and output.
1. Assuming that the differences are normally distributed, use Stata to find a 95% confidence interval for the Difference variable.

1. Keeping in mind that the Difference variable represents the Before cholesterol level minus the After level (i.e., a positive Difference is a reduction in cholesterol), what can you say about the effectiveness of the diet in reducing cholesterol?  In other words, based on your computed confidence interval can you say that the difference is significantly greater than 0?  Explain why.

1. Run a one-sample t-test (using the Difference variable) and use the resulting p-value to assess if the diet results in reduced cholesterol levels.  Use a significance level, a, of 0.05.  The null and alternative hypotheses, respectively are H0: m = 0 vs. H1: m > 0 .  Clearly communicate the relevant p-value, how this p-value compares to the significance level, and your conclusion (i.e., if you reject or fail to reject the null hypothesis).

1.  Suppose a clinical trial is conducted to test the efficacy of a new drug for treating gonorrhea.  46 patients are given a 4g daily dose of the drug and are seen 1 week later, at which time 6 of the patients still have gonorrhea.  Construct a 95% confidence interval for the proportion of patients that have gonorrhea after treatment.  Assume you can use the normal (Wald) approximation.

1. The mean and standard deviation serum creatinine level measured in 12 patients, 24 hours after they received a newly proposed antibiotic, was 1.2 mg/dL and 0.6 mg/dL, respectively.  You may assume that the levels follow a normal distribution.  If the mean serum creatinine in the general population is 1.0 mg/dL, test if the mean serum creatinine level in this patient group is significantly different from that of the general population.  Use a significance level of 0.05.  Report the relevant p-value matching your alternative hypothesis and state your conclusion (i.e., reject or fail to reject the null hypothesis).

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