is there any systematic tendency for part-time college faculty to hold their students to different standards than do full-time faculty? an article reported that for a sample of 125 courses taught by full-time faculty, the mean course gpa was 2.7286 and the standard deviation was 0.66342, whereas for a sample of 88 courses taught by part-timers, the mean and standard deviation were 2.8439 and 0.52241, respectively. does it appear that true average course gpa for part-time faculty differs from that for faculty teaching full-time? test the appropriate hypotheses at significance level 0.01.

Respuesta :

At α = 0.01 ; the result is insignificant.

H0 : μ1 - μ2 = 0

H1 : μ1 - μ2 ≠ 0

-1. 34

0.1837

Full time :

n1 = 125

x1 = 2.7386

s1 = 0.65342

Part time :

n2 = 88

x2 = 2.8439

s2 = 0.49241

H0 : μ1 - μ2 = 0

H1 : μ1 - μ2 ≠ 0

Test statistic :

The test statistic :

(x1 - x2) / sqrt[(s1²/n1 + s2²/n2)]

(2.7386 - 2.8439) / sqrt[(0.65342²/125 + 0.49241²/88)]

−0.1053 / sqrt(0.0034156615712 + 0.0027553)

-0.1053 /0.0785554

= - 1.34

Test statistic = - 1.34

The P value :

Using df = smaller n - 1 = 88 - 1 = 87

P value from test statistic score ;

P value = 0.1837

P value > α ; We fail to reject the null and conclude that the GPA does not differ.

At α = 0.01 ; the result is insignificant.

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