Question

At a university the historical mean of scholarship examination scores for freshman applications is 800. A historical population standard deviation  σ = 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 of 90 applications provided a sample mean x = 834?

(c) Use the confidence interval to conduct a hypothesis test. Using  α = 0.05,  what is your conclusion?

(d) What is the test statistic? What is the p-value?

Answer 1

a) The appropriate hypotheses are -

against

b)

c) Since the lower bound of the confidence interval < 800, so we reject the null hypothesis at 95% level of confidence or at 5% level of significance and we can conclude that mean of scholarship examination scores for freshman applications has significantly been changed from 800.

d)