Answer to Question #132958 in Statistics and Probability for Aditya

Question

Fifteen trainees in a technical program are randomly assigned to three different types of
instructional approaches, all of which are concerned with developing a specified level of skill
in computer-assisted design. The achievement test scores at the conclusion of the
instructional unit are reported in Table along with the mean performance score associated
with each instructional approach. Use the analysis of variance procedure to test the null
hypothesis that the three-sample means were obtained from the same population, using the
5 percent level of significance for the test.

Answer 1

We have the sample of the scores of 15 students (First Group, Second Group, Third Group). Each group consists of 5 students. We calculate the mean of each group. We should find out whether these means are different significantly (whether they were chosen from the different populations), $\alpha=0.05.$

$H_0:\mu_1=\mu_2=\mu_3\\ H_1:\text{ at least one of the means is different}.$

Using Single-Factor ANOVA in Excel we get $p$-value$\approx 0.57>\alpha.$ So we accept $H_0.$

Three different types of the instructional approaches have the same effect on the students.

For generating the values we used NORMINV(RAND(); 70; 5) in Excel.