Suppose a student organization at a university collected data for a study involving class sizes from different departments. The following table shows the average class size from a random sample of classes in the business school vs. the average class size from a random sample of classes in the engineering school. Data for the sample sizes and standard deviations are also shown. Use this data to complete parts a through c. Business Engineering Sample mean 38.1 32.7 Sample standard deviation 10.2 11.6 Sample size 17 21 a. Perform a hypothesis test using o = 0.01 to determine if the average class size differs between these departments. Assume the population variances for the number of students per class are not equal. Determine the null and alternative hypotheses for the test. Ho: H1 - H2 = 0 H1 : H1 - H2 # 0 Calculate the appropriate test statistic and interpret the result. The test statistic is 1.52 . (Round to two decimal places as needed.) The critical value(s) is(are)]. (Round to two decimal places as needed. Use a comma to separate answers as needed.)Because the test statistic the null hypothesis. The average business class size is the average engineering class size. o. louruy me p-value from part a and erpret wie result. The p-value is] (Round to three decimal places as needed.) Interpret the result. Choose the correct answer below. O A. Since the p-value is equal to or greater than the significance level, reject the null hypothesis. O B. Since the p-value is less than the significance level, reject the null hypothesis. O C. Since the p-value is equal to or greater than the significance level, do not reject the null hypothesis. O D. Since the p-value is less than the significance level, do not reject the null hypothesis. c. What assumptions need to be made in order to perform this procedure? O A. Since the sample sizes are large enough, no assumptions are needed. O B. Although the sample size in the first sample is large enough, it must be assumed that the distribution for the second sample is normally distributed. O C. If both sample sizes are not each at least 30, then one must assume that the underlying populations are normally distributed to perform this procedure. Also, one must assume that the samples are independent. O D. Although the sample size in the second sample is large enough, it must be assumed that the distribution for the first sample is normally dietrinidad