Question

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 2.7186 and the standard deviation was 0.66342, whereas for a sample of 88 courses taught by part-timers, the mean and standard deviation were 2.8639 and 0.49241, 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.

State the relevant hypotheses.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u_{Full tIme} = u_{Part Time}
Alternative hypothesis: u_{Full tIme} ? u_{Part Time}

Note that these hypotheses constitute a two-tailed test.  

Formulate an analysis plan. For this analysis, the significance level is 0.01. Using sample data, we will conduct a two-sample z-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), z statistic test statistic (z).

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]
SE = 0.07922
z = [ (x₁ - x₂) - d ] / SE

z = - 1.83

where s₁ is the standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is the size of sample 1, n₂ is the size of sample 2, x₁ is the mean of sample 1, x₂ is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.

Since we have a two-tailed test, the P-value is the probability that a z statistic more extreme than -1.83; that is, less than -1.83 or greater than 1.83.

Thus, the P-value = 0.067.

Interpret results. Since the P-value (0.067) is more than the significance level (0.01), we have to accept the null hypothesis.