You may need to use the appropriate appendix table or technology to answer this question.

At Western University the historical mean of scholarship examination scores for freshman applications is 900. A historical population standard deviation

= 180

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.

H₀: 900

H_a: < 900

H₀: 900

H_a: > 900

H₀: = 900

H_a: 900

H₀: < 900

H_a: 900

H₀: > 900

H_a: 900

(b)What is the 95% confidence interval estimate of the population mean examination score if a sample of 200 applications provided a sample mean

x = 936?

(Round your answers to the nearest integer.) ........to ........ ?

(c) Use the confidence interval to conduct a hypothesis test. Using

= 0.05,

what is your conclusion?

Do not reject H₀. There is insufficient evidence to conclude that the mean examination score for the new freshman applications has changed.

Do not reject H₀. There is sufficient evidence to conclude that the mean examination score for the new freshman applications has changed.

Reject H₀. There is sufficient evidence to conclude that the mean examination score for the new freshman applications has changed.

Reject H₀. There is insufficient evidence to conclude that the mean examination score for the new freshman applications has changed.

(d)What is the test statistic? (Round your answer to two decimal places.).......?

What is the p-value? (Round your answer to four decimal places.)

p-value = ....?