Question

Statistics I – Second Analysis Project

You are part of a research team that is interested in comparing the effectiveness of two different methods for teaching physical science to middle school students. In particular, they wish to compare two individualized computer based instruction programs. One is based on behavioristic principles while the other is based on principles of cognitive theories. A sample of students is randomly selected. Individuals in the sample are then randomly assigned to one of the two instructional programs. After completing the computer-based instruction each student is given the new state physical science test. Although there are many outcomes of potential interest, this study focuses on achievement as measured by the state physical science achievement test.

The research team wishes to estimate the size of the effect and to conduct a statistical test with a set to .05. For this project you should analyze the data and write a short summary of the results. Please turn in (1) the summary, (2) the program, and (3) the output.

Behavioristic Program Participants	Cognitive Program Participants
640 600 560 580 520 440 540 600 450 570 440 470 730 560 610 390 520 500 550 590 500 630 610 490 450 520 580 560 380	400 660 440 410 500 430 570 230 570 450 610 500 510 470 610 320 550 440 430 370 480 520 400 410 500 640 460 530 530

Answer 1

Here we have two independent samples so here we used the two-sample t-test.

Using Minitab statistical software

Hypothesis:

H0: Mean of Behavioristic Program Participants and Cognitive Program Participants are equal

H1: Mean of Behavioristic Program Participants and Cognitive Program Participants are not equal

Test statistic:

Two-Sample T-Test and CI: Behavioristic, cognitive

Two-sample T for Behavioristic vs cognitive

SE
N Mean StDev Mean
Behavioristic 29 537.2 79.1 15
cognitive 29 481.7 96.8 18

Difference = μ (Behavioristic) - μ (cognitive)
Estimate for difference: 55.5
95% CI for difference: (9.0, 102.1)
T-Test of difference = 0 (vs ≠): T-Value = 2.39 P-Value = 0.020 DF = 53

here p value 0.020<0.05 so we reject H0( Null hypothesis) so we say there is statistical difference between two treatments.

conclusion:

The effectiveness of two different methods of Behavioristic Program Participants and Cognitive Program Participants are not equal