Respuesta :
Answer:
The alternative hypothesis H0, should be rejected, if sample mean, X' < 25.051
Step-by-step explanation:
Given:
Sample size, n = 40
Mean, μ = 27
Significance level = 0.02
Standard deviation = 6
For null hypothesis :
H0 : μ ≥ 27
For alternative hypothesis :
H1 : μ < 27
At significance level, α = 0.02, from Z table, Zα = 2.054
This is a left tailed test
Solving for X' we have:
[tex] X' = u - Za \frac{\sigma}{\sqrt{n}}[/tex]
[tex] X' = 27 - 2.054 \frac{6}{\sqrt{40}}= 25.051[/tex]
The alternative hypothesis H0, should be rejected, if sample mean, X' < 25.051
The rejection rule is based on the value of for the test to determine whether the manufacturer's claim should be rejected is [tex]\mu<27[/tex].
Given :
- The sample size is 40.
- .02 level of significance.
- The mean is 27.
- The standard deviation is 6.
The following steps can be used in order to determine the rejection rule based on the value of the test:
Step 1 - The Hypothesis test can be used in order to determine the rejection rule based on the value of the test.
The null hypothesis is given below:
[tex]H_0 : \mu\geq 27[/tex]
The alternate hypothesis is given below:
[tex]H_a : \mu<27[/tex]
Step 2 - Now, the formula of X' is given below:
[tex]X' = \mu-Z_\alpha \dfrac{\sigma}{\sqrt{n} }[/tex]
Step 3 - Now, substitute the values of the known terms in the above formula.
[tex]X' = 27-2.054 \dfrac{6}{\sqrt{40} }[/tex]
Step 4 - SImplify the above expression.
[tex]X' = 25.051[/tex]
From the above steps, it can be concluded that the null hypothesis is rejected.
For more information, refer to the link given below:
https://brainly.com/question/10758924
