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]