In the past,of all the students enrolled in "Basic Business Statistics" 10% earned A's 20% earned B's,30% earned C's,20% earned D's and the rest either failed or withdrew from the course.Dr Johnson is a new professor teaching "Basic Business Statistics" for the first time this semester.At the conclusion of the semester,in Dr.Johnson's class of 60 students,there were 10 A's,20 B's,20 C's,5 D's and 5 W's or F's.Assume that Dr.Johnson's class constitutes a random sample.Dr Johnson wants to know if there is sufficient evidence to conclude that the grade distribution of his class is different than the historical grade distribution. At $\alpha$ = .05,test to determine if the grade distribution for Dr.Johnson's class is different than the historical grade distribution. A)Reject H₀ B)Fail to reject H₀

Question

Quizplus · Accepted Answer

We will use a chi-square goodness-of-fit test to compare the grade distribution of Dr. Johnson's class to the historical grade distribution.

The expected frequencies for each grade category can be calculated as follows:

Expected number of A's: 0.1 x 60 = 6
Expected number of B's: 0.2 x 60 = 12
Expected number of C's: 0.3 x 60 = 18
Expected number of D's: 0.2 x 60 = 12
Expected number of W's or F's: 0.2 x 60 = 12

To calculate the chi-square statistic, we use the formula:

χ2 = ∑ [(Oi - Ei)2 / Ei]

where Oi is the observed frequency for each grade category and Ei is the expected frequency for each grade category.

Using the observed and expected frequencies, we obtain:

χ2 = [(10-6)2/6] + [(20-12)2/12] + [(20-18)2/18] + [(5-12)2/12] + [(5-12)2/12] 
= 6.33

The degrees of freedom for this test is df = 5-1 = 4 (since there are 5 categories and we are estimating one parameter).

Using a chi-square distribution table with df = 4 and α = 0.05, we find that the critical value of χ2 is 9.488.

Since our calculated χ2 (6.33) is less than the critical value (9.488), we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the grade distribution of Dr. Johnson's class is different than the historical grade distribution.

In the Past,of All the Students Enrolled in "Basic Business α\alphaα

In the Past,of All the Students Enrolled in "Basic Business $\alpha$