Answer: C) [tex]\chi^2=52.02[/tex]
Step-by-step explanation:
Given : It is desired to determine if the population standard deviation exceeds 20 minutes.
i.e. [tex]H_a: \sigma>20[/tex]
Here, we perform chi-square test.
Sample size : n= 51
Sample standard deviation : s= 20.40
The test statistic for chi-square test is given by :-
[tex]\chi^2=\dfrac{(n-1)s^2}{\sigma^2}[/tex]
, where n= sample size
s= sample standard deviation.
[tex]\sigma[/tex]= Population standard deviation.
Substitute the values , we get
[tex]\chi^2=\dfrac{(51-1)(20.40)^2}{(20)^2}\\\\=\dfrac{50\times 416.16}{400}=52.02[/tex]
Hence, the test statistic for this test of hypothesis= [tex]\chi^2=52.02[/tex]
Thus , the correct answer is C) [tex]\chi^2=52.02[/tex]
