Instructions: Round all your m
Instructions: Round all your math steps to two decimal placesjust like I have been doing in class.
Consider the following hypothesis test:
H0: µ ≤ 25
Ha: µ > 25
A sample of 40 provided a sample mean of 26.4. The populationstandard deviation is 6.
a. Compute the value of the test statistic. (Round to twodecimal 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 (Rejectthe null) or (do not reject the null hypothesis).
Answer:
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 isconcluded that the null hypothesis is fails to reject.
It is concluded that the null hypothesis Ho is notrejected. Therefore, there is not enough evidence to claimthat the population
mean μ is greater than 25, at the 0.01 significancelevel.
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