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5. College instructors prefer to have their students participate actively in class. In a remote learning setting, it is ideal to set synchronous online meeting once in a while. Suppose a researcher claims that the time of these synchronous meetings affects the students' participation. To test this claim, the researcher conducted an experiment of randomly assigning 40 students to 4 different timeslots of online meetings. Student participation was measured by counting the number of times students asked and answered questions. The data is presented below. 8:00 A.M. 10:00 A.M. 1:00 P.M. 4:00 P.M. 11 14 8 8 14 16 7 W 10 13 8 4 10 15 8 14 & 11 6 9 8 O 13 11 13 14 6 11 9 18 9 14 12 6 5 7 16 7 9 Is there sufficient evidence for the claim of the researcher to be true at 5% level of significance? Assume normality. 6. Answer any two of the following: a. Materials requirement planning systems are computerized planning and control system for manufacturing operations. These systems are used to manage raw materials and work-in process inventories while improving customer service. Suppose you want to estimate the proportion p of manufacturing firms that use these systems. Approximately how large a sample would be required to estimate p to within 0.02 with 90% confidence level? b. Hospital administrators wish to learn the average length of stay of all surgical patients. A statistician determines that, for a 95% confidence level estimate of the average length of stay to within 0.5 days, 50 surgical patient's records will have to be examined. How many records should be looked at to obtain a 95% confidence level estimate to within 0.25 days? c. A politician wants to know what percentage of the voters support her position on the issue of divorce. What size voter sample should be obtained to determine with 90% confidence the support level to within 4%