Answer:
b. between .025 and .05
Step-by-step explanation:
Previous concepts and notation
The chi-square test is used to check if the standard deviation of a population is equal to a specified value. We can conduct the test "two-sided test or a one-sided test".
represent the sample mean
n = 30 sample size
s= 0.2 represent the sample deviation
the value that we want to test
represent the p value for the test
t represent the statistic
significance level
State the null and alternative hypothesis
On this case we want to check if the population standard deviation is less than 0.027, 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:
![t=(30-1) [\frac{0.2}{0.164}]^2 =42.963](https://tex.z-dn.net/?f=%20t%3D%2830-1%29%20%5B%5Cfrac%7B0.2%7D%7B0.164%7D%5D%5E2%20%3D42.963)
What is the approximate p-value of the test?
The degrees of freedom are given by:
For this case since we have a right tailed test the p value is given by:
And the best option would be:
b. between .025 and .05
