Question

Consider the following hypothesis test.

H0: μ ≤ 25

Ha: μ > 25

A sample of 40 provided a sample mean of 26.1. The population standard deviation is 6.

(a) Find the value of the test statistic. (Round your answer to two decimal places.)

(b) Find the p-value. (Round your answer to four decimal places.) p-value =

(c) At α = 0.01,state your conclusion.

(d)

State the critical values for the rejection rule. (Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic≤

test statistic≥

State your conclusion.

Answer 1

Solution :

= 25

=26.1

=6

n = 40

This is the right tailed test .

The null and alternative hypothesis is ,

H0 :    ≤ 25

Ha : > 25

a )Test statistic = z

= ( - ) / / n

= (26.1-25) / 6 / 40

= 1.16

Test statistic = z = 1.16

b ) P(z > 1.16 ) = 1 - P(z < 1.16 ) = 1 -0.8770

P-value =0.1230

c ) = 0.01

P-value >

0.1230 > 0.01

Reject the null hypothesis .

There is sufficient evidence to suggest that

d ) The rejection region for this right-tailed test is R={z:z>2.33

It is observed that z =1.16 ≤ zc​=2.33,