Question 1; uu..n'1T1..3Tu.JT1r1TJ Ju..y lui'll'l'al An marketing scientist is interested in nding there is a relationship between supermarkets and the number of hours spent by customers. The scientist created the following contingency table from a suwey of customers shopping at three diEt'erent markets versus four different categories of time in hours spent in the shops. Each cell represents the count of customers shopping in a supermarket in a period of time. TIME SPENT Less than 1 Between 1 to Between 2 and 3 Greater than 3 hours less than 2 hours hours hours Coles 65 l 68 67 SUPERMARKETS Woolworths 66 2 59 67 Aldi 59 3 71 70 a) What is the null hypothesis for this test? [0.5 marlG] b) The expected values (correct to 5 decimal places) for the contingency table based on the null hypothesis is shown below. . Calculate the missing expected counts and show your working out. Full justication is required to gain full marks for this part. Show the working out in your uploaded pages. [1.0 mark] TIME SPENT Less than I Between 1 to Between 2 and 3 Greater than 3 hours less than 2 hours hours hours Coles A B 66.55184 68.56856 SUPERMAst Woolworths C I) 64.23411 66.l 8060 Aldi 64.49833 2.036789 67.21405 69.25084 c) Calculate the test statistic. Full justication is required to gain full marks for this part. Show the working out in your uploaded pages. [1.5 mark] d) Calculate the pvalue of the test. Full justication is required to gain full marks for this part. Show the working out in your uploaded pages. [0.5 mark] e) What is the conclusion of the test. Choose all plausihle options. [1.0 mark] The supermarkets and the time spent may be independent There is no evidence ofa relationship between supermarkets and the time spent. There is signicant evidence of a relationship between supermarkets and the time spent. There is evidence to suggest of a relationship between supermarkets and the time spent. There is insuicient evidence to suggest ofa relationship between supermarkets and the time spent. The supermarkets and the time spent are dependent The supermarkets and the time spent are independent 1) In addition, the marketing scientist is interested in nding whether proportion of customers in each category of time spent are equal when differences among supermarkets are not considered. . Provide the table of counts for the "time spent per week" variable from the data given above. Full justication is required to gain full marks for this part. Show the working out in your uploaded pages. [1.0 mark] g) Use the data table you created for the previous question to test Whether the proportion ofeustomers in each category of time spent are equal when differences between categories of supermarkets are not considered. Full justication is required to gain full marks for this part. Show the working out in your uploaded pages. [1.0 mark]