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The owners of a shopping mall had studied the shopping habits of their customers. Historical data showed that the mean time spent by shoppers in the mall was 60 minutes. The owners improved the mall and wished the improvement would cause shoppers to spend more time in the mall. A random sample of 50 shoppers is selected, the average time spent by these shoppers in the mall is 62 minutes with a standard deviation of 5 minutes.
(a) Use p-value approach, is there evidence to suggest that the improvement has caused shoppers to spend more time in the mall at 5% level of significance?
(b) Explain why the sampling distribution of sample mean follow the normal distribution in this case.
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