Question

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 P-value. Use ?_employed ? ?_{not employed}. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value 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?

Answer 1

H₀:

H₁:

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

P-value = P(T < -1.84)

             = 0.0335

As the P-value 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.