Question

(Refer to HW4, #4) 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.
Is the mean amount of money spent by all customers at this supermarket is higher than $65 after
the campaign? Perform the hypothesis testing at 1% significance level by answering the following
questions.
(a) Formulate the null and alternative hypothesis.
(b) State the test statistic and its approximate distribution.
(c) Determine the critical value for α = .01 and state the decision rule.
(d) Calculate the observed value of the test statistic from the sample.
(e) State whether H0 is rejected and tell why.
(f) Calculate the P-value and do the hypothesis testing based on the P-value.
(g) Express the conclusion in the context of the problem, using common English

Answer 1