In a study of the effect of college student employment on academic performance,

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 mu_employed - mu_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.)

Explanation / Answer

Solution:

Let 1 be the mean for employed

Let 2 be the mean for not employed

Ho: 1=2

Ha: 1 2

The test statistic is

t=(x1-x2)/(s1/n1+s2/n2)

=(3.22-3.33)/sqrt(0.485^2/176+0.524^2/116)
=-1.81

The degree of freedom df = n1+n2-2=176+116-2 =290

The p-value= 2*P( t with df=290 <-1.81) = 0.0713 (from student t table)

Assume a=0.05

Since the p-value is larger than 0.05, we do not reject Ho.

So we can not conclude there is a significant difference between employed and not employed.

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