# Air Force Training Program

Air Force Training Program

You are an instructor at the U.S. Air Force Academy, teaching courses in introductory electronics. Your teaching methods so far have involved giving your students a videotaped lecture followed by a programmed instruction text. Each student works independently at his/her own pace. After completing the content in the text, each student must then pass a final test.

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You have noticed that some students are able to complete the self-paced programmed instruction text very quickly, whereas other students take much longer with the text and require additional time to complete the course. Students who work faster must then wait for the students who work slower, since the entire cohort proceeds together with other aspects of their training. This creates downtime for the faster-working students and at times even harms group morale.

After thinking about this problem, you propose an alternative instructional strategy that uses computer-assisted instruction. In this method, you decide that all your students will continue to view the videotaped lecture first, but then in lieu of the programmed text, each student will be assigned to a computer for additional instruction. The computer will guide the students, who are working independently, through the self-training part of your course.

To compare the current and proposed instructional methods for your course, you decide to conduct an experiment. The entering class of 122 students will be randomly assigned to one of the two teaching methods; 61 students will follow your traditional programmed text method and the 61 other students will follow the new computer-assisted method. You will record the time (in hours) each student takes to complete the course content. The exam will not be included in the total time.

After completing the experiment, you calculated descriptive statistics for each group.

You conducted a hypothesis test about the mean difference between the two instructional method means using the sample standard deviations. Your analysis generated Figure 11.2.1. In addition, you constructed a 95% confidence interval for the mean difference as represented in Figure 11.2.2. How would you best explain these figures to your direct superior in the Air Force?

FIGURE 11.2.1 p-value for the mean difference between programmed text and computer-based methods

FIGURE 11.2.2 95% Confidence Interval for the mean difference between programmed text and computer-based methods

FIGURE 11.2.2 95% Confidence Interval for the mean difference between programmed text and computer-based methods

 ROPOSE THAT THE MEANS OF THE TWO METHODS ARE NOT SIGNIFICANTLY DIFFERENT. A P-VALUE OF 0.452 IS GREATER THAN  = 0.05 OFFERS EVIDENCE FOR THIS CONCLUSION. ALSO, A MEAN OF ZERO IS WITHIN THE 95% CONFIDENCE INTERVAL FOR THE DIFFERENCE.
 I PROPOSE THAT THE MEANS OF THE TWO METHODS ARE NOT SIGNIFICANTLY DIFFERENT. A P-VALUE OF 0.548 IS GREATER THAN  = 0.05 OFFERS EVIDENCE FOR THIS CONCLUSION. ALSO, A MEAN OF ZERO IS WITHIN THE 95% CONFIDENCE INTERVAL FOR THE DIFFERENCE.
 I PROPOSE THAT THE MEANS OF THE TWO METHODS ARE NOT SIGNIFICANTLY DIFFERENT. A P-VALUE OF 0.025 IS LESS THAN  = 0.05 OFFERS EVIDENCE FOR THIS CONCLUSION. ALSO, A MEAN OF ZERO IS WITHIN THE 95% CONFIDENCE INTERVAL FOR THE DIFFERENCE.
 I PROPOSE THAT THE MEANS OF THE TWO METHODS ARE SIGNIFICANTLY DIFFERENT. A P-VALUE OF 0.452 IS GREATER THAN  = 0.05 OFFERS EVIDENCE FOR THIS CONCLUSION. ALSO, A MEAN OF ZERO IS NOT WITHIN THE 95% CONFIDENCE INTERVAL FOR THE DIFFERENCE.

Air Force Training Program

You are an instructor at the U.S. Air Force Academy, teaching courses in introductory electronics. Your teaching methods so far have involved giving your students a videotaped lecture followed by a programmed instruction text. Each student works independently at his/her own pace. After completing the content in the text, each student must then pass a final test.

You have noticed that some students are able to complete the self-paced programmed instruction text very quickly, whereas other students take much longer with the text and require additional time to complete the course. Students who work faster must then wait for the students who work slower, since the entire cohort proceeds together with other aspects of their training. This creates downtime for the faster-working students and at times even harms group morale.

After thinking about this problem, you propose an alternative instructional strategy that uses computer-assisted instruction. In this method, you decide that all your students will continue to view the videotaped lecture first, but then in lieu of the programmed text, each student will be assigned to a computer for additional instruction. The computer will guide the students, who are working independently, through the self-training part of your course.

To compare the current and proposed instructional methods for your course, you decide to conduct an experiment. The entering class of 122 students will be randomly assigned to one of the two teaching methods; 61 students will follow your traditional programmed text method and the 61 other students will follow the new computer-assisted method. You will record the time (in hours) each student takes to complete the course content. The exam will not be included in the total time.

After completing the experiment, you calculated descriptive statistics for each group.

To further

instructional methods, you offer decision makers the following summary

information and accompanying distribution graph:

= 0.05

FIGURE 11.4 Two-tailed F distribution with 60 degrees of freedom in the numerator and 60 degrees of freedom in the denominator, upper and lower critical values,  = 0.05

Which of the following actions/explanations would best summarize your information to the assembled decision makers?

 ACCORDING TO MY ANALYSIS, WHILE THE MEANS FOR BOTH METHODS WERE similar, the variance or spread of the computer-based method was nearly 2.5 times that of the programmed text method. As you can see, the F = 1.67 is far above the lower critical value of Fcritical = 0.60, placing F = 1.67 in the region of the distribution where H0 must be rejected. The probability that the difference in variance is due to random chance is low.
 ACCORDING TO MY ANALYSIS, WHILE THE MEANS FOR BOTH METHODS WERE similar, the variance or spread of the programmed text method was nearly 1.5 times that of the computer-based method. As you can see, the F = 2.48 is far above the upper critical value of Fcritical = 1.67, placing F = 2.48 in the region of the distribution where H0 cannot be rejected. The probability that the difference in variance is due to random chance is high.
 ACCORDING TO MY ANALYSIS, WHILE THE MEANS FOR BOTH METHODS WERE similar, the variance or spread of the programmed text method was nearly 2.5 times that of the computer-based method. As you can see, the F = 2.48 is far above the upper critical value of Fcritical = 1.67, placing F = 2.48 in the region of the distribution where H0 must be rejected. The probability that the difference in variance is due to random chance is low.
 ACCORDING TO MY ANALYSIS, THE MEANS FOR BOTH METHODS WERE SIMILAR AND the variance or spread of the two methods were also similar. As you can see, the F = 1.67 is far below the upper critical value of Fcritical = 2.48, placing F = 1.67 in the region of the distribution where H0 cannot be rejected. The probability that the difference in variance is due to random chance is high.

Air Force Training Program

You are an instructor at the U.S. Air Force Academy, teaching courses in introductory electronics. Your teaching methods so far have involved giving your students a videotaped lecture followed by a programmed instruction text. Each student works independently at his/her own pace. After completing the content in the text, each student must then pass a final test.

You have noticed that some students are able to complete the self-paced programmed instruction text very quickly, whereas other students take much longer with the text and require additional time to complete the course. Students who work faster must then wait for the students who work slower, since the entire cohort proceeds together with other aspects of their training. This creates downtime for the faster-working students and at times even harms group morale.

After thinking about this problem, you propose an alternative instructional strategy that uses computer-assisted instruction. In this method, you decide that all your students will continue to view the videotaped lecture first, but then in lieu of the programmed text, each student will be assigned to a computer for additional instruction. The computer will guide the students, who are working independently, through the self-training part of your course.

To compare the current and proposed instructional methods for your course, you decide to conduct an experiment. The entering class of 122 students will be randomly assigned to one of the two teaching methods; 61 students will follow your traditional programmed text method and the 61 other students will follow the new computer-assisted method. You will record the time (in hours) each student takes to complete the course content. The exam will not be included in the total time.

After completing the experiment, you calculated descriptive statistics for each group.

To test for the equality of the population variances between the two methods, you first establish the following hypothesis test using  = 0.05:

Completing the F-test for Two Equal Variances in Excel produced the following output:

Based on this output, what conclusion would you offer the decision-makers in the Air Force training program?

 FAIL TO REJECT H0. THE VARIANCES BETWEEN THE TWO METHODS ARE NOT SIGNIFICANTLY DIFFERENT. THE F-CRITICAL TWO-TAILED OF 3.06 IS HIGHER THAN THE TEST STATISTIC F = 2.48; THEREFORE, THE NULL HYPOTHESIS CANNOT BE REJECTED BECAUSE F DOES NOT EXCEED THE CRITICAL VALUE.
 REJECT H0. THE VARIANCES BETWEEN THE TWO METHODS ARE SIGNIFICANTLY DIFFERENT. THE TWO-TAILED P-VALUE IS 0.0006, WHICH IS LESS THAN  = 0.05.
 FAIL TO REJECT H0. THE VARIANCES BETWEEN THE TWO METHODS ARE NOT SIGNIFICANTLY DIFFERENT. THE ONE-TAILED P-VALUE IS 0.9997, WHICH IS GREATER THAN  = 0.05.
 REJECT H0. THE VARIANCES BETWEEN THE TWO METHODS ARE SIGNIFICANTLY DIFFERENT. THE F-CRITICAL TWO-TAILED OF 1.24 IS LOWER THAN THE TEST STATISTIC F = 1.53; THEREFORE, THE NULL HYPOTHESIS CAN BE REJECTED BECAUSE F EXCEEDS THE CRITICAL VALUE.

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