Question

QUESTION 2 Provide an appropriate response. Compute the standardized test statistic, X 2 , to test the claim σ 2 ≤ 16 if n = 20, s 2 = 31 , and 36.813 12.82 33.41 9.322 20 points

Answer 1

Answer:  36.813

Step-by-step explanation:

Given claim : $\sigma^2\leq16$

Then , the set of hypothesis for this claim will be :-

$\H_0:\sigma^2\leq16\\\\H_a:\sigma^2>16$.

The formula to find the standardized chi-square test statistic ( $\chi^2$ ) will be :_

$\chi^2=\dfrac{(n-1)s^2}{\sigma^2}$

Given :$n=20\ ;\ s^2=31$

Then $\chi^2=\dfrac{(20-1)(31)}{16}=36.8125\approx36.813$

Hence, the standardized test statistic $\chi^2=36.813$