A student asked a statistics professor if grades were marked "on the curve." The professor decided to give the student a project to determine if last year's statistics grades were normally distributed. The professor told the student that last year's mean mark was 70 with a standard deviation of 10 and to use the following results. What is your decision if $\alpha$ = 0.05?
A) The letter grades are evenly distributed.
B) The letter grades are not evenly distributed.
C) The letter grades are normally distributed.
D) The letter grades are not normally distributed.
E) The letter grades are unfairly distributed.

Question

A student asked a statistics professor if grades were marked "on the curve." The professor decided to give the student a project to determine if last year's statistics grades were normally distributed. The professor told the student that last year's mean mark was 70 with a standard deviation of 10 and to use the following results.  What is your decision if $\alpha$ = 0.05?
A) The letter grades are evenly distributed. 
B) The letter grades are not evenly distributed. 
C) The letter grades are normally distributed. 
D) The letter grades are not normally distributed. 
E) The letter grades are unfairly distributed.

Quizplus · Accepted Answer

To determine whether the grades are normally distributed, we need to conduct a hypothesis test. Since the sample size is not given, we can assume that it is sufficiently large (in practice, a sample size of at least 30 is considered large enough).

The null hypothesis is that the grades are normally distributed, and the alternative hypothesis is that they are not normally distributed.

We can use a normal probability plot or a Shapiro-Wilk test to test for normality. According to the given normal probability plot, the data points do not fall on a straight line, indicating that the data are not normally distributed. This is confirmed by the Shapiro-Wilk test, which gives a significance value of 0.0397. Since this value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the grades are not normally distributed. Therefore, the answer is D, the letter grades are not normally distributed.

A Student Asked a Statistics Professor If Grades Were Marked α\alphaα

A Student Asked a Statistics Professor If Grades Were Marked $\alpha$