Question

7.38 Teaching descriptive statistics. A study compared five different methods for teaching descriptive statistics. The five methods were traditional lecture and discussion, programmed textbook instruction, programmed text with lectures, computer instruction, and computer instruction with lectures. 45 students were randomly assigned, 9 to each method. After completing the course, students took a 1-hour exam. (a) What are the hypotheses for evaluating if the average test scores are different for the different teaching methods? (b) What are the degrees of freedom associated with the F-test for evaluating these hypotheses? (c) Suppose the p-value for this test is 0.0168. What is the conclusion?

Answer 1

A study compared five different methods for teaching descriptive statistics.

The five methods were traditional lecture and discussion, programmed textbook instruction, programmed text with lectures, computer instruction, and computer instruction with lectures.

for k=5, there are 5 treatments, k = 5

45 students were randomly assigned, 9 to each method. After completing the course, students took a 1-hour exam.

total number of observations = n = 45

a)

we want to test that the average test scores are different for the different teaching methods.

Ho:- The average test scores are the same for the different teaching methods.

Vs

Ha:- The average test scores are different for the different teaching methods.

b)

The degrees of freedom associated with the F-test are degrees of freedom for treatment & for the error

degrees of freedom for treatment = k-1 = 5-1= 4

degrees of freedom for the error = n-k = 45- 5 = 40

F test have df = 4,40

c) The p-value for this test is 0.0168.

We reject Ho if P-value < level of significance

i) for levels of significance = 0.05

P-value=0.0168 < level of significance=0.05

We reject Ho

we may conclude that the average test scores are different for the different teaching methods.

ii) for levels of significance = 0.01

P-value=0.0168 >  level of significance=0.01

We fail to reject Ho

we may conclude that the average test scores are not different for the different teaching methods.