Answer:
No. There is not enough evidence to support the claim that the population standard deviation is different from $12.
Step-by-step explanation:
The null hypothesis is that the true standard deviation is 12.
The alternative hypothesis is that the true standard deviation differs from 12.
We can state:
[tex]H_0: \sigma=12\\\\H_a: \sigma\neq12[/tex]
The significance level is 0.10.
The sample size is n=15, so the degrees of freedom are:
[tex]df=n-1=15-1=14[/tex]
The sample standard deviation is 9.25.
The test statistic is
[tex]T=(n-1)(s/\sigma_0)^2=14*(9.25/12)^2=14*0.77^2=14*0.59=8.32[/tex]
The critical values for rejecting the null hypothesis are:
[tex]\chi_{0.025,13}=5.00875\\\\\chi_{0.975,13}=24.7356[/tex]
As T=8.32 is within the acceptance region (5.01, 24.74), the null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the population standard deviation is different from $12.
