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 2.7386 and the standard deviation was 0.65342, 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

The question is regarding a hypothesis test to compare the true average course GPAs between part-time and full-time college faculty. We set up null and alternative hypotheses and use a t-test to determine if there's a statistically significant difference in GPAs at a significance level of 0.01.

Step-by-step explanation:

To test whether there is a systematic tendency for part-time college faculty to hold their students to different standards than full-time faculty, we need to compare the average course GPA for part-time faculty to that of full-time faculty. We can do this by conducting a hypothesis test.

The null hypothesis (H0) is that the true average course GPA for part-time faculty is the same as that for full-time faculty. The alternative hypothesis (Ha) is that the true average course GPA for part-time faculty differs from that for full-time faculty.

To test these hypotheses, we can use a two-sample t-test since we have independent samples from two different populations. We will test the hypotheses at a significance level of 0.01.

First, we calculate the test statistic using the formula:

t = (mean1 - mean2) / sqrt((variance1/n1) + (variance2/n2))

where mean1 and mean2 are the sample means, variance1 and variance2 are the sample variances, and n1 and n2 are the sample sizes. Plugging in the given values:

t = (2.8639 - 2.7386) / sqrt((0.49241/88) + (0.65342/125))

Next, we compare the calculated test statistic to the critical value from the t-distribution with (n1 + n2 - 2) degrees of freedom at the 0.01 significance level. If the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.