In: Math
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?
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)