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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
(a) Determine the five number summary of this sample.
(b) What assumption will have to be made if we want to construct a confidence interval for the mean time spent by all shoppers in the mall? Explain.
(c) Construct an 80% confidence interval for the mean time spent by all shoppers in the mall. Interpret the result.
(d) Based on the result of part (c), at 20% level of significance, should we reject the null hypothesis for = 75 minutes? Explain.
(e) In order to make the estimation of population mean corrected to within ±3 minutes at 95% confidence, what is the minimum sample size?
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