At a university the historical mean of scholarship examinationscores for freshman applications is 800. A historical populationstandard deviation  σ = 150 is assumed known.Each year, the assistant dean uses a sample of applications todetermine whether the mean examination score for the new freshmanapplications has changed.
(a) State the hypotheses.
(b) What is the 95% confidence interval estimate of thepopulation mean examination score if a sample of 90 applicationsprovided a sample mean x = 834?
(c) Use the confidence interval to conduct a hypothesis test.Using  α = 0.05,  what is yourconclusion?
(d) What is the test statistic? What is thep-value?
