Case Problem Air Force Training Program An Air Force introductory course in elec

Question

Case Problem Air Force Training Program An Air Force introductory course in electronics uses a personalized system of instruction whereby each student views a videotaped lecture and then is given a programmed instruction text. The students work independently with the text until they have completed the training and passed a test. Of concern is the varying pace at which the students complete this portion of their training program. Some students are able to cover the programmed instruction text relatively quickly, whereas other students work much longer with the text and require additional time to complete the course. The fast students wait until the slow students complete the introductory course before the entire group proceeds together with other aspects of their training. A proposed alternative system involves use of computer-assisted instruction. In this method, all students view the same videotaped lecture and then each is assigned to a computer terminal for further instruction. The computer guides the student, working independently, through the self-training portion of the course. To compare the proposed and current methods of instruction, an entering class of 122 students was assigned randomly to one of the two methods. One group of 61 students used the current programmed-text method and the other group of 61 students used the proposed computer-assisted method. The time in hours was recorded for each student in the study.

The following data are provided in the WEBfile named Training. Training Course Completion Times (hours) for Current Training Method

76 76 77 74 76 74 74 77 72 78 73 78 75 80 79 72 69 79 72 70 70 81 76 78 72 82 72 73 71 70 77 78 73 79 82 65 77 79 73 76 81 69 75 75 77 79 76 78 76 76 73 77 84 74 74 69 79 66 70 74 72

Course Completion Times (hours) for Proposed Computer-Assisted Method

74 75 77 78 74 80 73 73 78 76 76 74 77 69 76 75 72 75 72 76 72 77 73 77 69 77 75 76 74 77 75 78 72 77 78 78 76 75 76 76 75 76 80 77 76 75 73 77 77 77 79 75 75 72 82 76 76 74 72 78 71

Managerial Report Use appropriate descriptive statistics to summarize the training time data for each method.

What similarities or differences do you observe from the sample data? Use the methods of Chapter 10 to comment on any difference between the population means for the two methods. Discuss your findings.

Compute the standard deviation and variance for each training method.

Conduct a hypothesis test about the equality of population variances for the two training methods. Discuss your findings. What conclusion can you reach about any differences between the two methods?

What is your recommendation? Explain.

Can you suggest other data or testing that might be desirable before making a final decision on the training program to be used in the future?

Explanation / Answer

We are given the two methods :

1) Training Course Completion Times (hours) for Current Training Method

2) Course Completion Times (hours) for Proposed Computer-Assisted Method

We have to find mean and standard deviation of the two methods.

This we can find by using MINITAB.

steps :

Enter all the data in MINITAB sheet --> Stat --> Basic statistics --> Display descriptive statistics --> variable : select two methods --> statistics : select mean and standard deviation --> ok --> ok

Descriptive Statistics: x, y

Variable Mean StDev
x 75.066 3.945
y 75.426 2.506

We see that mean of two methods are approximately same.

standard deviation of method 1 = 3.945

standard deviation of method 2 = 2.506

Hypotheiss for the test is,

H0 : Variances are equal.

H1 : Variances are not equal.

Assume alpha = 5% = 0.05

MINITAB steps :

Stat --> Basic statistics --> 2-Variances --> Samples in different column --> First : x --> second : y --> options --> Confidence level : 95% --> ok --> ok

Output is :

F-Test (normal distribution)
Test statistic = 2.48, p-value = 0.001

p-value < alpha

Reject H0 at 5% level of significance.

Conclusion :  Variances are not equal.

From this result we also test two mean using two sample t-test and unpooled variances.

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