At a university the historical mean of scholarship examination scores for freshman applications is800. A historical population standard deviation=150

is assumed known. Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.

(a)

State the hypotheses.

(b)

What is the 95% confidence interval estimate of the population mean examination score if a sample of100applications provided a sample meanx=833?

(c)

Use the confidence interval to conduct a hypothesis test. Using= 0.05,

what is your conclusion?

(d)

What is the test statistic? What is thep-value?