Question

Consider the following hypothesis test:

Answer 1

Answer:

$z=\frac{27.4-26}{\frac{6}{\sqrt{40}}}=1.48$  

The p value can be founded with the following probability:

$p_v =P(z>1.476)=0.0694$  

Step-by-step explanation:

Information given

$\bar X=27.4$ represent the sample mean  

$\sigma=6$ represent the population deviation

$n=40$ sample size  

$\mu_o =26$ represent the value to verify

z would represent the statistic

$p_v$ 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:$\mu \leq 26$  

Alternative hypothesis:$\mu > 26$  

The statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)  

Replacing the info we got:

$z=\frac{27.4-26}{\frac{6}{\sqrt{40}}}=1.48$  

The p value can be founded with the following probability:

$p_v =P(z>1.476)=0.0694$