Question

12.15.  Undergraduate students in a large state university are required to take an introduction to psychology course. Three sections of this course are offered at the same time and are taught by three different instructors. The chi square test is used to determine if any of these sections has significantly more students, which may indicate that the instructor of that section is more popular than the other two instructors. The enrollment figures for the three sections are presented in the following table. The chi square value is 6.29 (c²=6.29) significant at the p<.05 level.

INSTRUCTOR	NUMBER OF STUDENTS ENROLLED
Dr. Smith	114
Dr. Brown	128
Dr. Johnson	91

a.        Which chi square test should be used to determine whether any of the sections has a statistically significantly higher number of students? Explain.

b.        What are the expectedfrequencies?

c.           What are the degrees of freedom (df)?

d.           What are your conclusions? Explain.

Answer 1

a) hre we will apply chi square goodness of fit test to check if all sections have equal proportions or one of the sections has higher proportion of students then other,.

b)expected frequenct for each category=np=(114+128+91)*(1/3)=111

c)degree of freedom =categories-1=3-1=2

d)for 0.05 level and 2 df ; critical value =5.991

as test statisic 6.29 is higher than critical value we reject null hypothesis of equal proportion

we have sufficient evidence at 0.05 level to conclude that any of the sections has a statistically significantly higher number of students