Respuesta :
Answer:
[tex]z=\frac{37.3-36.9}{\frac{2.2}{\sqrt{240}}}=2.817[/tex]
[tex]p_v =2P(z>2.817)=0.005[/tex]
since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is different from 36.9 mpg at 1% of significance.
Step-by-step explanation:
Data given and notation
[tex]\bar X=37.3[/tex] represent the sample mean
[tex]\sigma=2.2[/tex] represent the sample population deviation
[tex]n=240[/tex] sample size
[tex]\mu_o =36.9[/tex] represent the value that we want to test
[tex]\alpha=0.01[/tex] represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
System of hypothesis
We need to conduct a hypothesis in order to check if the true mean is different from 36.9 mpg, the system of hypothesis are:
Null hypothesis:[tex]\mu = 36.9[/tex]
Alternative hypothesis:[tex]\mu \neq 36.9[/tex]
The statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]z=\frac{37.3-36.9}{\frac{2.2}{\sqrt{240}}}=2.817[/tex]
P-value
Since is a two sided test the p value would be:
[tex]p_v =2P(z>2.817)=0.005[/tex]
Conclusion
since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is different from 36.9 mpg at 1% of significance.
