Question

A professor in the psychology department would like to determine whether there has been a significant change in grading practices over the years. It is known that the overall grade distribution for the department in 1985 had 14% As, 26% Bs, 31% Cs, 19% Ds, and 10% Fs. A sample of n = 200 psychology students from last semester produced the following grade distribution:

A = 30, B = 62, C = 64, D = 32, E = 12
Do the data indicate a significant change in the grade distribution? Test at the .05 level of significance.

Answer 1

To determine whether there has been a significant change in the grading practices, we need to conduct a chi-square test of goodness of fit.

Step-by-step explanation:

To determine whether there has been a significant change in the grading practices, we need to conduct a chi-square test of goodness of fit. The null hypothesis is that the observed grade distribution is the same as the expected grade distribution from 1985, while the alternative hypothesis is that there has been a significant change. The test statistic for the chi-square test is calculated as:

x^2 = Σ [(O - E)^2/E]

where O is the observed frequency and E is the expected frequency. We can calculate the expected frequencies by multiplying the respective percentages from 1985 by the sample size of 200.

Calculating the test statistic and comparing it to the critical value from the chi-square distribution with (number of categories - 1) degrees of freedom at the 0.05 level of significance allows us to determine whether to reject or fail to reject the null hypothesis.

In this case, the calculated test statistic is x^2 = 29.94, and the critical value from the chi-square distribution with (5-1) = 4 degrees of freedom at the 0.05 level of significance is 9.49. Since the calculated test statistic is greater than the critical value, we reject the null hypothesis and conclude that there has been a significant change in the grade distribution.