Do male and female students study the same amount per week I

Do male and female students study the same amount per week? In 2007, 58 sophomore business students were surveyed at a large university that has more than 1,000 sophomore business students each year.

At the 0.05 level of significance, is there a difference in the variance of the study time for male students and female students?

1. Please report the test statistic for the appropriate test.

2. Please report the critical value for the appropriate test.

3. Please report the p-value for the appropriate test.

4. Is there sufficient evidence?

5. Which t-test is appropriate for comparing the mean study time for male and female students?

Solution

Getting the standard deviation of the males and females,

s1 (female) = 5.714420816
s2 (male) = 5.406386824

We use the F test here.

Formulating the null and alternative hypotheses,              
              
Ho:   sigma1^2 / sigma2^2   =   1  
Ha:    sigma1^2 / sigma2^2   =/   1  
              
As we can see, this is a    two   tailed test.      
              
              
1.

Getting the test statistic, as              
s1 =    5.714420816          
s2 =    5.406386824          
              
Thus, F = s1^2/s2^2 =    1.117198146   [ANSWER, TEST STATISTIC]

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2.

Thus, getting the critical F, as alpha =    0.05   ,      
alpha/2 =    0.025          
df1 = n1 - 1 =    19         
df2 = n2 - 1 =    37          
F (crit) =    0.425905614   and   2.116850078   [ANSWER, CRITICAL VALUES]

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3.

Getting the P value, as this is two tailed,

P = 0.749242547 [ANSWER]

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4. No, as P > 0.05, there is no sufficient evidence that there is a difference in the variance of the study time for male students and female students.

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5. We can use a 2-sample independent samples t test. [ANSWER]