Question

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 ?

Answer 1

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