Question

Marks assigned by an economics lecturer to students taking her post-graduate subject at a university in New South Wales have historically followed a distribution with 5% HDs, 25% Ds, 40% Cs, 25% Ps and 5% Fs. This year, a sample of grades revealed 11 HDs, 32 Ds, 62 Cs, 29 Ps and 16 Fs. Can you conclude, at the 1% level of significance, that this year’s marks are distributed differently from marks in the past?

Answer 1

To determine if this year's grades are distributed differently from historical trends, a chi-square goodness of fit test comparing the observed and expected frequencies of grades would be used, with conclusions drawn at the 1% significance level.

Step-by-step explanation:

A student has inquired if the grades distributed for their post-graduate economics subject at a university in New South Wales this year show a different distribution from historical trends. The historical distribution of grades is 5% HDs, 25% Ds, 40% Cs, 25% Ps, and 5% Fs. This year's sample has 11 HDs, 32 Ds, 62 Cs, 29 Ps, and 16 Fs. To answer this question, we would typically use a chi-square goodness of fit test to compare the observed frequencies of grades with the expected frequencies based on historical data.

Using the chi-square test, we calculate the expected number of grades in each category based on the sample size and compare these with the actual numbers reported. At the 1% level of significance, we would determine if there are statistically significant differences between the observed and expected frequencies. This process allows us to draw conclusions about whether this year's grade distribution is significantly different from historical trends.