The federal government would like to test the hypothesis that the standard deviation for the age of men filing for Social Security is higher than the standard deviation for the age of women. The following table summarizes sample statistics from each population.
Women 
Men 

Sample standard deviation 
2.6 years 
3.3 years 
Sample size 
24 
20 
Using
alpha?equals=?0.10,
what is the critical value for this hypothesis? test?
A.
Since the test statistic is less than the? critical? value, we reject the null hypothesis and cannot conclude that the standard deviation for the age of men filing is higher than the standard deviation for the age of womens.
B.
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 men filing is higher than the standard deviation for the age of womens.
C.
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 men filing is higher than the standard deviation for the age of womens.
D.
Since the test statistic is more than the? critical? value, we fail to reject the null hypothesis and cannot conclude that the standard deviation for the age of men filing is higher than the standard deviation for the age of womens.
Null Hypothesis
Alternative Hypothesis
Since , We consider in the numerator and in denominator
Therefore, Degrees of Freedom = (n11), (n21) = (19,23)
The critical value of F for (19,23) df , at 10% significance level is 1.7525
Under H0, the test statistic is
Conclusion :
B. 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 men filing is higher than the standard deviation for the age of womens.
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