The manager of a consulting firm is trying to assess the effectiveness of comput
ID: 3183596 • Letter: T
Question
The manager of a consulting firm is trying to assess the effectiveness of computer skills training given to all new entry-level professionals. In an effort to make such an assessment, he administers a computer skills test immediately before and after the training program to each of 20 randomly chosen employees.
The pre-training and post-training scores of these 20 individuals are shown in the table.
A. Is this two-sample data or paired data? Explain your answer.
B. Specify an appropriate hypothesis test.
C. Using a 10% level of significance, do the given sample data support that the firm’s training programs is effective in increasing the new employee’s computer skills?
D. Using a 1% level of significance, do the given sample data support that the firm’s training programs is effective in increasing the new employee’s working knowledge of computing?
Employee Score before Score after 1 62 77 2 63 77 3 74 83 4 64 88 5 84 80 6 81 80 7 54 83 8 61 88 9 81 80 10 86 88 11 75 93 12 71 78 13 86 82 14 74 84 15 65 86 16 90 89 17 72 81 18 71 90 19 85 86 20 66 92Explanation / Answer
(A)
The given data is the paired data where same subjects were used in both evaluation before training and after training.
(B)
Below are the null and alternate hypothesis
H0: Mean(after) <= Mean(before)
H1: Mean(after) > Mean(before)
Mean(difference) = 11
std. dev. (diff) = 11.0024
value to test statistics, t = 11/(11.0024/sqrt(20)) = 4.4712
p - value = 0.00013
As p-value is less than 0.1(significance level), we reject the null hypothesis. Similarly for 0.01 significance level. This means there is significant evidence that training improves the employee skills.
Employee Score before Score after Difference 1 62 77 15 2 63 77 14 3 74 83 9 4 64 88 24 5 84 80 -4 6 81 80 -1 7 54 83 29 8 61 88 27 9 81 80 -1 10 86 88 2 11 75 93 18 12 71 78 7 13 86 82 -4 14 74 84 10 15 65 86 21 16 90 89 -1 17 72 81 9 18 71 90 19 19 85 86 1 20 66 92 26Related Questions
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