Question

Consider the following hypothesis test.

H0: μ ≤ 25

Ha: μ > 25

A sample of 40 provided a sample mean of 26.6. 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. Chose one of the following.

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. Chose one of the following.

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:
Given in the question
Null hypothesis H0: mean <=25
Alternate hypothesis Ha: mean>25
Sample size = 40
Sample mean = 26.6
Population standard deviation = 6
Solution(a)
Test stat = (Sample mean - Population mean)/standard deviation/sqrt(n) = (26.6-25)/6/sqrt(40) = 1.69
Solution(b)
Here we will use Z test as no. of sample is greater than 30 and population standard deviation is known
From Z table we found p-value = 0.0455 and this is one sample test
Solution(c)
at alpha=0.01, we can not reject null hypothesis as p-value is greater than 0.01, there is insufficient evidence to conclude that mean>25. So its answer is D. i.e. Do not reject H0, there is insufficient evidence to conclude that mean >25
Solution(d)
at alpha = 0.01 and this is one tailed test so test static>=2.575(This is rejection region)
As we can see that test stat value is less than 2.575 so we are failed to reject H0.
So its answer is D. i.e. Do not reject H0. these is insufficient evidence to conclude that mean>25