A researcher wants to know whether fraternity brothers and sorority sisters volunteer the same amount of time, on average. The data below shows how many hours each group volunteered. Use a significance level of 0.10 and assume the data follows a normal distribution. The population standard deviation (\sigma ) is unknown. Round answers to 3 decimal places. Using a ti-84 calculator write or show all inputs.
Fraternity Brothers \mu B: 8, 9, 6, 14, 7, 6, 14, 12, 8, 3, 9, 11, 9
Sorority Sisters \mu S: 13, 13, 19, 6, 4, 9, 14, 7, 7, 14, 18, 15, 19
1.Write the null and alternative hypotheses.
2.What is the critical values for this test? (Use the t-distribution with appropriate degrees of freedom).
3.Find the test statistic.
4.What is the p-value?
5.Give two explanations to support your conclusion. (Use the comparison between the test statistic and critical value, and the p-value vs. significance level.) Also find and explain the difference of the 2 samples.