Answer: 36.813
Step-by-step explanation:
Given claim : [tex]\sigma^2\leq16[/tex]
Then , the set of hypothesis for this claim will be :-
[tex]\H_0:\sigma^2\leq16\\\\H_a:\sigma^2>16[/tex].
The formula to find the standardized chi-square test statistic ( [tex]\chi^2[/tex] ) will be :_
[tex]\chi^2=\dfrac{(n-1)s^2}{\sigma^2}[/tex]
Given :[tex]n=20\ ;\ s^2=31[/tex]
Then [tex]\chi^2=\dfrac{(20-1)(31)}{16}=36.8125\approx36.813[/tex]
Hence, the standardized test statistic [tex]\chi^2=36.813[/tex]
