Consider the following hypothesis test:

H0: ≤ 26
Ha: > 26

A sample of 40 provided a sample mean of 27.4. The population standard deviation is 6.

Compute the value of the test statistic (to 2 decimals).
What is the p-value (to 4 decimals)?

Answer :

Answer:

[tex]z=\frac{27.4-26}{\frac{6}{\sqrt{40}}}=1.48[/tex]  

The p value can be founded with the following probability:

[tex]p_v =P(z>1.476)=0.0694[/tex]  

Step-by-step explanation:

Information given

[tex]\bar X=27.4[/tex] represent the sample mean  

[tex]\sigma=6[/tex] represent the population deviation

[tex]n=40[/tex] sample size  

[tex]\mu_o =26[/tex] represent the value to verify

z would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to check if the true mean for this case is higher than 26, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 26[/tex]  

Alternative hypothesis:[tex]\mu > 26[/tex]  

The statistic is given by:

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)  

Replacing the info we got:

[tex]z=\frac{27.4-26}{\frac{6}{\sqrt{40}}}=1.48[/tex]  

The p value can be founded with the following probability:

[tex]p_v =P(z>1.476)=0.0694[/tex]  

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