## Related questions with answers

Question

Use the sample results from the previous problem to test the claim that the generated values are from a population with a standard deviation equal to $12.5$. Use a $0.05$ significance level.

Solution

VerifiedStep 1

1 of 2$H_0:\sigma=12.5$

$H_1:\sigma\neq 12.5$

Compute the value of the test statistic:

$\chi^2=\dfrac{n-1}{\sigma^2_0}s^2=\dfrac{100-1}{12.5^2}\cdot 11.7^2=86.734$

Determine the critical value(s) using table VII with $df=n-1=100-1=99$:

$\chi^2_{1-0.025}=\chi^2_{0.975}=74.222$

$\chi^2_{0.025}=129.561$

If the test statistic is in the rejection region, then reject the null hypothesis:

$74.222<86.734<129.561\Rightarrow \text{ Do not reject } H_0$

There is not sufficient evidence to reject the claim.

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