Suppose Sony would like to test the hypothesis that the standard deviation for the age of PlayStation users is higher than the standard deviation for the age of Xbox users. The following table summarizes sample statistics from each population.
Playstation 
Xbox 

Sample standard deviation 
6.5years 
1.9 years 
Sample size 
25 
28 
Using
alpha?equals=?0.05,
what is the conclusion for this hypothesis? test?
A.
Since the test statistic is more than the critical? value, we reject the null hypothesis and cannot conclude that the standard deviation for the age of PlayStation users is higher than the standard deviation for the age of Xbox users.
B.
Since the test statistic is less than the critical? value, we fail to reject the null hypothesis and conclude that the standard deviation for the age of PlayStation users is higher than the standard deviation for the age of Xbox users.
C.
Since the test statistic is less than the critical? value, we fail to reject the null hypothesis and cannot conclude that the standard deviation for the age of PlayStation users is higher than the standard deviation for the age of Xbox users.
D.
Since the test statistic is more than the critical? value, we fail to reject the null hypothesis and conclude that the standard deviation for the age of PlayStation users is higher than the standard deviation for the age of Xbox users.
Here we need to do F test. So hypotheses are :
Test is right tailed.
Here we have
Test statistics wil be
Degree of freedom of numerator: df1=n1 1 = 24
Degree of freedom of denominator: df2=n2 1 = 27
The pvalue is: 0.0000
The critical value is; 1.930
Since F is greater than critical value so we reject the null hypothesis.
Since the test statistic is more than the critical? value, we reject the null hypothesis and can conclude that the standard deviation for the age of PlayStation users is higher than the standard deviation for the age of Xbox users.
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