Answer:
![t=(15-1) [\frac{0.219}{0.2}]^2 =16.7864](https://tex.z-dn.net/?f=%20t%3D%2815-1%29%20%5B%5Cfrac%7B0.219%7D%7B0.2%7D%5D%5E2%20%3D16.7864)
And the 2 is because we are conducting a bilateral test.
since the the 
we fail to reject the null hypothesis.
since the the 
we fail to reject the null hypothesis.
Step-by-step explanation:
Data given
population mean (variable of interest)
represent the population standard deviation
represent the sample deviation
n=15 represent the sample size
represent the values for the significance level
Hypothesis test
On this case we want to check if the population standard deviation is equal or not to 0.2, so the system of hypothesis are:
H0: 
H1: 
In order to check the hypothesis we need to calculate the statistic given by the following formula:
![t=(n-1) [\frac{s}{\sigma_o}]^2](https://tex.z-dn.net/?f=%20t%3D%28n-1%29%20%5B%5Cfrac%7Bs%7D%7B%5Csigma_o%7D%5D%5E2%20)
This statistic have a Chi Square distribution distribution with n-1 degrees of freedom.
What is the value of your test statistic?
Now we have everything to replace into the formula for the statistic and we got:
P value
We know the degrees of freedom of the distribution 14 on this case and we can find the p value like this:
And the 2 is because we are conducting a bilateral test.
since the the we fail to reject the null hypothesis.
since the the we fail to reject the null hypothesis.
