To compare two programs for training industriaal workers to perform a skilled job, 20 workers are included in an experiment. Of these, 10 are selected at random and trained by method 1; the remaining 10 workers are trained by method 2. After competion , all workers are subjected to a time -and - metion test that records the speed of performance of a skilled job. The followind data are obtained
method 1 | 15 20 11 23 16 21 18 16 27 24
method 2 | 23 31 13 19 23 17 28 26 25 28
Can you conclude from data that the mean job time is significiant difference after training with method 1 than after method 2?
a) State the null hypothesis and alternative hyphotesis
b) Find the test statistic
c) If the type I error a=0.05 , find the critical velue(s) and draw the rejection region(s)
d) Base on the type I error a , given above , what is the conlusion ?
a)
b)
t-Test: Two-Sample Assuming Equal Variances | ||
method 1 | method 2 | |
Mean | 19.1 | 23.3 |
Variance | 23.21111111 | 30.9 |
Observations | 10 | 10 |
Pooled Variance | 27.05555556 | |
Hypothesized Mean Difference | 0 | |
df | 18 | |
t Stat | -1.805535636 | |
P(T<=t) one-tail | 0.043872141 | |
t Critical one-tail | 1.734063607 | |
P(T<=t) two-tail | 0.087744282 | |
t Critical two-tail | 2.10092204 |
test statistic = -1.805535636
c)
critical values are 2.10092204 and -2.10092204
rejection region TS > 2.10092204 or TS < - 2.10092204
d)
since TS does not lie in critical region
we fail to reject the null hypothesis
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