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

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=((n-1)s^2)/(\sigma^2)`

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

Then
`\chi^2=((20-1)(31))/(16)=36.8125\approx36.813`

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