Question

• The following are the weekly losses of work-hours due to accidents in 10 industrial plants before and after a certain safety program were put into operation

Before	45	73	46	124	33	57	83	34	26	17
After	36	60	44	119	35	51	77	29	24	11

1. Is the assumption that the difference in weekly losses of work-hours is normally distributed reasonable?
2. Test whether the safety program is effective. Use α=0.05.
3. Find a 95% confidence interval on the difference in mean weekly losses of work-hours.

Answer 1

Ans a ) using minitab>Graph>boxplot

we have

from the boxplot, we can say that the assumption that the difference in weekly losses of work-hours is normally distributed is reasonable.

2 ) let d = before - after

the null and alternative hypothesis is

Ho:ud = 0

Ha:ud 0

using minitab<Stat>basic stat>paired t

we have

Paired T-Test and CI: Before, After

Paired T for Before - After

N Mean StDev SE Mean
Before 10 53.8 32.1 10.1
After 10 48.6 31.0 9.8
Difference 10 5.20 4.08 1.29

95% CI for mean difference: (2.28, 8.12)
T-Test of mean difference = 0 (vs ≠ 0): T-Value = 4.03 P-Value = 0.003

the value of test statistic is 4.03

p value is 0.003

since p value is less than 0.05 so we reject Ho and conclude that the safety program is effective

3 ) a 95% confidence interval on the difference in mean weekly losses of work-hours is (2.28,8.12)

since confidence interval does not contain 0 so we can conclude that  the safety program is effective