A country report claims that the mean monthly expenses for a family of 4 is US$2,500 per month. You believe that the mean cost is more than US$2,500 per month. You randomly selected a sample of 300 families of 4 and found out the mean cost is US$2,750 with a standard deviation of $350. Assuming that the population is normally distributed, test, at the 10% level of significance, whether the report is underestimating the mean monthly expenses for a family of 4, by answering the following:
(a) State the null and alternative hypotheses for the test.
(b) Calculate the test statistics.
(c) Determine the rejection region(s) for the test.
(d) State the conclusion for the test giving reasons for your answer.