Question

Suppose a student organization at the University of Illinois collected data for a study involving class sizes from different departments. A random sample of 11 classes in the business department had an average size of 38.1 students with a sample standard deviation of 10.6 students. A random sample of 12 classes in the engineering department had an average size of 32.6 students with a sample standard deviation of 13.2 students

a. Perform a hypothesis test using a = 0.05 to deter-mine if the average class size differs between these departments. Assume the population variances for the number of students per class are not equal.
b. Approximate the p-value using Table 5 in Appen-dix A and interpret the results.
c. Determine the precise p-value using Excel.

d. What assumptions need to be made in order to perform this procedure?

Answer 1

b)

see yourself , use df = 21 ,   TS = 1.106

c)

p-value = 2 P(t > |TS|)

= 0.2819

d)

Independent Samples T Test

· Assumption of Independence: you need two independent, categorical groups that represent your independent variable. In the above example of test scores “males” or “females” would be your independent variable.

· Assumption of normality: the dependent variable should be approximately normally distributed. The dependent variable should also be measured on a continuous scale. In the above example on average test scores, the “test score” would be the dependent variable.

· Assumption of Homogeneity of Variance: The variances of the dependent variable should be equal.