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Question 5 (23 marks) The owner of a shopping mall studied the shopping habits of his customers. In order to estimate the mean time spent by shoppers, a random sample of 10 shoppers is selected and their time spent (in minutes) in the mall are as follows: 73.2 59.8 46.7 53.4 69.8 45.6 64.5 50.2 64.8 27.9 (3) Determine the five number summary of this sample. (5 marks) (b) What assumption will have to be made if we want to construct a condence interval for the mean time spent by all shoppers in the mall? Explain. (4 marks) ) Construct an 80% confidence interval for the mean time spent by all shoppers in the mall. Interpret the result. (7 marks) (d) Based on the result of part (c), at 20% level of significance, should we reject the null hypothesis for u = 75 minutes? Explain. (3 marks) (e) In order to make the estimation of population mean corrected to within 13 minutes at 95% confidence, what is the minimum sample size? (4 marks)