Question

Instructions: Round all your math steps to two decimal places just like I have been doing in class.

Consider the following hypothesis test:

H₀: µ ≤ 25

H_a: µ > 25

A sample of 40 provided a sample mean of 26.4. The population standard deviation is 6.

a. Compute the value of the test statistic. (Round to two decimal places). Answer

b. What is the p-value? (Round to four decimal places). Answer

c. At α=0.01, what is your conclusion? Answer Choices (Reject the null) or (do not reject the null hypothesis).

Answer 1

Solution :

Given that,

Population mean = = 25

Sample mean = = 26.4

Population standard deviation = = 6

Sample size = n = 40

Level of significance = = 0.01

This is a right tailed test.

a.

The test statistics,

Z = ( - )/ (/)

= (26.4 - 25 ) / ( 6 / 40)

= 1.48

b.

P-value = P(Z > z )

= 1 - P(Z < 1.48)

= 1 - 0.9306

= 0.0694

c.

Do not reject the null hypothesis.

The p-value is p = 0.0694, and since p = 0.0694 ≥ 0.01, it is concluded that the null hypothesis is fails to reject.

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population

mean μ is greater than 25, at the 0.01 significance level.