1. In a study designed to test the effectiveness of garlic for lowering cholesterol, 49 adults were treated with garlic tablets. Cholesterol levels were measured before and after the treatment. The changes in their LDL cholesterol (in mg/dL) have a mean of 3 and standard deviation of 14. Construct a 95% confidence interval estimate of the mean change in LDL cholesterol after the garlic tablet treatment. Show all work. Just the answer, without supporting work, will receive no credit.

2. Mimi is interested in testing the claim that banana is the favorite fruit for more than 50% of the adults. She conducted a survey on a random sample of 100 adults. 58 adults in the sample chose banana as their favorite fruit.
Assume Mimi wants to use a 0.10 significance level to test the claim.

(a) Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the claim that banana is the favorite fruit for more than 50% of the adults? Explain.

3. In a pulse rate research, a simple random sample of 81 men results in a mean of 75 beats per minute, and a standard deviation of 12 beats per minute. Based on the sample results, the researcher concludes that the pulse rates of men have a standard deviation greater than 10 beats per minutes. Use a 0.05 significance level to test the researcher's claim.

(a) Identify the null hypothesis and alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the researcher's claim? Explain.