Question

1. A data set includes data from student evaluations of courses. The summary statistics are n=85​, x=3.44​, s=0.67. Use a 0.01 significance level to test the claim that the population of student course evaluations has a mean equal to 3.50. Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

a. determine the test statistic

b. determine the P-value ( round to 3 decimal places)

2. A data set about speed dating includes​ "like" ratings of male dates made by the female dates. The summary statistics are n=188​, x =7.87​, s=1.92. Use a 0.05 significance level to test the claim that the population mean of such ratings is less than 8.00. Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

a. determine the test statistic

b. determine the P-value ( round to 3 decimal places)

3.

In a test of the effectiveness of garlic for lowering​ cholesterol, 81 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes​ (before minus​ after) in their levels of LDL cholesterol​ (in mg/dL) have a mean of 0.9
and a standard deviation of 18.2. Use a 0.10 significance level to test the claim that with garlic​ treatment, the mean change in LDL cholesterol is greater than 0. What do the results suggest about the effectiveness of the garlic​ treatment? Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

a. determine the test statistic

b. determine the P-value ( round to 3 decimal places)

Answer 1

in problem ( 2 ) p value = 0.177