Question

Consider the following hypothesis test.

H0: μ ≤ 25

Ha: μ > 25

A sample of 40 provided a sample mean of 26.4. 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.

Reject H₀. There is sufficient evidence to conclude that μ > 25.Reject H₀. There is insufficient evidence to conclude that μ > 25.      Do not reject H₀. There is sufficient evidence to conclude that μ > 25.Do not reject H₀. There is insufficient evidence to conclude that μ > 25.

(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.

Reject H₀. There is sufficient evidence to conclude that μ > 25.Reject H₀. There is insufficient evidence to conclude that μ > 25.      Do not reject H₀. There is sufficient evidence to conclude that μ > 25.Do not reject H₀. There is insufficient evidence to conclude that μ > 25.

Answer 1

Solution :

= 25

= 26.4

= 6

n = 40

This is the right  tailed test .

The null and alternative hypothesis is

H0 :   ≤ 25

Ha : > 25

a) Test statistic = z

= ( - ) / / n

= (26.4 -25 ) /6 / 40

= 1.48

b) p(Z >1.48) = 1-P (Z <1.48 ) = 0.0694

P-value = 0.0694

= 0.05  

0.0694> 0.05

c) Do not reject H0. There is insufficient evidence to conclude that μ > 25.

d) Do not reject H0. There is insufficient evidence to conclude that μ > 25.