An Air Force introductory course in electronics uses a personalized system of in
ID: 3330021 • Letter: A
Question
An Air Force introductory course in electronics uses a personalized system of instruction whereby each student views a videotaped lecture and 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 involved 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 us the proposed computer-assisted method. The time in hours was recorded for each student in the study. The following data are provided in the data set Training.
Current
Proposed
76
74
76
75
77
77
74
78
76
74
74
80
74
73
77
73
72
78
78
76
73
76
78
74
75
77
80
69
79
76
72
75
69
72
79
75
72
72
70
76
70
72
81
77
76
73
78
77
72
69
82
77
72
75
73
76
71
74
70
77
77
75
78
78
73
72
79
77
82
78
65
78
77
76
79
75
73
76
76
76
81
75
69
76
75
80
75
77
77
76
79
75
76
73
78
77
76
77
76
77
73
79
77
75
84
75
74
72
74
82
69
76
79
76
66
74
70
72
74
78
72
71
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 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 difference 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 uses in the future?
Current
Proposed
76
74
76
75
77
77
74
78
76
74
74
80
74
73
77
73
72
78
78
76
73
76
78
74
75
77
80
69
79
76
72
75
69
72
79
75
72
72
70
76
70
72
81
77
76
73
78
77
72
69
82
77
72
75
73
76
71
74
70
77
77
75
78
78
73
72
79
77
82
78
65
78
77
76
79
75
73
76
76
76
81
75
69
76
75
80
75
77
77
76
79
75
76
73
78
77
76
77
76
77
73
79
77
75
84
75
74
72
74
82
69
76
79
76
66
74
70
72
74
78
72
71
Explanation / Answer
Descriptive statistics Current
count 61
mean 75.07
sample variance 15.56
sample standard deviation 3.94
minimum 65
maximum 84
range 19
Descriptive statistics Proposed
count 61
mean 75.43
sample variance 6.28
sample standard deviation 2.51
minimum 69
maximum 82
range 13
Given that,
sample 1
s1^2=15.56, n1 =61
sample 2
s2^2 =6.28, n2 =61
null, Ho: ^2 = ^2
alternate, H1: ^2 != ^2
level of significance, = 0.05
from standard normal table, two tailed f /2 =1.667
since our test is two-tailed
reject Ho, if F o < -1.667 OR if F o > 1.667
we use test statistic fo = s1^1/ s2^2 =15.56/6.28 = 2.48
| fo | =2.48
critical value
the value of |f | at los 0.05 with d.f f(n1-1,n2-1)=f(60,60) is 1.667
we got |fo| =2.478 & | f | =1.667
make decision
hence value of | fo | > | f | and here we reject Ho
ANSWERS
---------------
null, Ho: ^2 = ^2
alternate, H1: ^2 != ^2
test statistic: 2.48
critical value: -1.667 , 1.667
decision: reject Ho
we conclude that population variances for the two training methods are not equal
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