Question

A college admissions officer states that the average ACT score for incoming freshmen at her school is no more than 22 and that standard deviation for ACT scores is 4 points. A sample of 36 incoming freshmen reveals an average ACT score of 23.5. State the null and alternative hypotheses concerning this claim and test the hypothesis at the 99% confidence level using the P-value. Is the officer's statement correct, based on this sample information and your test?

Answer 1

H0: <= 22

Ha: > 22

Test statistics

z = - / / sqrt(n)

= 23.5 - 22 / 4 / sqrt(36)

= 2.25

This is test statistics value.

p-value = P( Z > z)

= P( Z > 2.25)

= 0.0122

Significance level = 1 - 0.99 = 0.01

Since p-value > 0.01 level , we do not have sufficient evidence to reject H0.

We conclude at 0.01 level that the officers statement is correct.