6. (12 marks) The university audit department would like to know if there is a significant difference in the mean hours worked per week by professors from different academic departments, viz. Architecture (A), Biology (B) and Chinese Literature (C). They recorded the number of hours worked in the previous week from a random sample of 5 different professors from each department in the following table: Professor | Architecture (A) Biology (B) Chinese Literature (C) 56 49 50 60 38 35 3 45 55 39 4 19 62 45 56 53 32 Mean 53.2 51.4 40.2 variance 36.7 78.3 53.7 Develop the null and alternative hypothesis. b. If the level of significant (a = 0.05), compute the test statistic. C. Using the critical value approach, what is the rejection rule? d. What is the conclusion from this test? Explain with the help of a diagram. 7. (8 marks) An e-commerce research company claims that 60% or more graduate students have bought merchandise on-line. A consumer group is suspicious of the claim and thinks that the proportion is lower than 60%, A random sample of 80 graduate students show that only 40 students have ever done so. What the sample proportion? b. What is our null hypothesis and test statistics? What is our rejection rule if we want to conduct the test at 10% Type I error rate. d. What is your conclusion