In a study of the effect of college student employment on academic performance, the following summary statistics for GPA were reported for a sample of students who worked and for a sample of students who did not work. The samples were selected at random from working and nonworking students at a university. (Use a statistical computer package to calculate the Pvalue. Use ?_{employed} ? ?_{not employed}. Round your test statistic to two decimal places, your df down to the nearest whole number, and your Pvalue to three decimal places.)
Sample Size 
Mean GPA 
Standard Deviation 

Students Who Are Employed 
176  3.22  0.485 
Students Who Are Not Employed 
118  3.33  0.514 
t  = 
df  = 
P  = 
Does this information support the hypothesis that for students at
this university, those who are not employed have a higher mean GPA
than those who are employed? Use a significance level of 0.05.
Yes OR No?
H_{0}:
H_{1}:
t = ()/sqrt(s1^2/n1 + s2^2/n2)
= (3.22  3.33)/sqrt((0.485)^2/176 + (0.514)^2/118)
= 1.84
df = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1  1) + (s2^2/n2)^2/(n2  1))
= ((0.485)^2/176 + (0.514)^2/118)^2/(((0.485)^2/176)^2/175 + ((0.514)^2/118)^2/117)
= 241
Pvalue = P(T < 1.84)
= 0.0335
As the Pvalue is less than the significance level (0.0335 < 0.05), we should reject the null hypothesis.
Yes, this information support the hypothesis that for students at this university, those who are not employed have a higher mean GPA than those who are employed.
Get Answers For Free
Most questions answered within 1 hours.