Question

The past records of a supermarket show that its customers spend an average of $65 per visit at this
store. Recently the management of the store initiated a promotional campaign according to which
each customer receives points based on the total money spent at the store and these points can be
used to buy products at the store. The management expects that as a result of this campaign, the
customers should be encouraged to spend more money at the store. To check whether this is true,
the manager of the store took a sample of 12 customers who visited the store. The following data
give the money (in dollars) spent by these customers at this supermarket during their visits.
88 69 141 28 106 45 32 51 78 54 110 83
Assume that the money spent by all customers at this supermarket has a normal distribution with
mean µ and variance σ
2
. Answer the following questions.
(a) Compute the sample mean and the sample standard deviation of the above sample.
(b) What are the estimators for µ and σ
2
?
(c) What are the estimates for µ and σ
2 based on this sample?
(d) Construct a 90% confidence interval for µ. What is the confidence based on?

Answer 1