8. (16 marks) While you arc deciding whether to enroll next term into section A or B of a class which is taught by the same teacher but at different time of the day, you wanted to know whether there is any difference in test scores. You took a sample of 30 students from section A and calculated the sample mean to be 82 and another sample of 40 students from section B and calculated the sample mean to be 78. You know that the population standard deviation of both section are the same at JA = 3; = 10. Formulate the null and alternative hypothesis. b. What is the value of the test statistic? C. At 95% confidence, what is the margin of error? d. With a = 0.05, what is your hypothesis testing conclusion? e. What if you don't know the population standard deviation, but you can calculate the sample standard deviation from your sample of 30 and 40 staklents from section A and B. What will be your test statistic, when your $1 - 10 and $2 = 12? What is the rejection rule with a = 0.05. 9. (20 marks) Most people like to drink coffee in order to consume caffeine. Four cups of coffee were tested from 3 difference coffee shops on campus and the amount of caffeine mg/ 8oz of coffee are shown below. Coffee Shop Sample A B C 1 87.5 95 85 2 95 40 85 3 92.5 $5 4 95 75 Mean 53.2 51.4 40.2 Variance 36.7 78.3 53.7 a. Compute the sum of squares due to treatments (SSTR). b. Compute the mean square due to treatments (MSTR). C. Compute the sum of squares due to crror (SSB). d. Compute the mean square due to error (MSE). C. At a = 0.05 level of significance, test whether the means for the three treatments are equal using critical valuc approach