Question

An engineer wants to determine the effectiveness of a safety program. He collects annual loss of hours due to accidents in 12 plants before and after the program was put into operation. Plant Before After Plant Before After 1 114 89 7 92 88 2 106 97 8 100 64 3 108 102 9 81 68 4 86 99 10 71 52 5 70 57 11 77 58 6 88 85 12 108 108 Click here for the Excel Data File Let the difference be defined as Before – After. a. Specify the competing hypotheses that determine whether the safety program was effective. H0: μD = 0; HA: μD ≠ 0 H0: μD ≤ 0; HA: μD > 0 H0: μD ≥ 0; HA: μD < 0 b-1. Calculate the value of the test statistic. Assume that the hours difference is normally distributed. (Round intermediate calculations to at least 4 decimal places and final to 2 decimal places.) b-2. Find the p-value. p-value < 0.01 p-value 0.10 0.05 p-value < 0.10 0.025 p-value < 0.05 0.01 p-value < 0.025 c. At the 5% significance level, is there sufficient evidence to conclude that the safety program was effective? Yes, since we reject H0. No, since we do not reject H0. Yes, since we do not reject H0. No, since we reject H0. rev: 09_19_2019_QC_CS-181378

Answer 1

H0: μD ≤ 0; HA: μD > 0

b-1)

S. No	Before	After	diff:(d)=x1-x2	d2
1	114	89	25	625.00
2	106	97	9	81.00
3	108	102	6	36.00
4	86	99	-13	169.00
5	70	57	13	169.00
6	88	85	3	9.00
7	92	88	4	16.00
8	100	64	36	1296.00
9	81	68	13	169.00
10	71	52	19	361.00
11	77	58	19	361.00
12	108	108	0	0.00
	total	=	Σd=134	Σd2=3292
	mean dbar=	d̅     =	11.1667
	degree of freedom =n-1                            =		11
	Std deviaiton SD=√(Σd2-(Σd)2/n)/(n-1) =		12.776636
	std error=Se=SD/√n=		3.6883
	test statistic            =	(d̅-μd)/Se         =	3.03

b-2)

p-value < 0.01

c)

Yes, since we reject H0.