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: μ_D = 0; H_A: μ_D ≠ 0

• H₀: μ_D ≤ 0; H_A: μ_D > 0

• H₀: μ_D ≥ 0; H_A: μ_D < 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.)

Answer 1

Ho: Mp 30:H: Up>0.

(6-1) EXCEL (Data Analysis) output: t-Test: Paired Two Sample for Means Mean Variance Observations Pearson Correlation Hypothesized Mean Difference Before After 91.75 80.58333333 234.3863636 389.1742424 12 0.76206132 t Stat PIT<=t) one-tail t Critical one-tail PIT<=t) two-tail t Critical two-tail 3.027594151 0.005749315 1.795884814 0.011498631 2.200985159 The value of the test statistic is t = 3.03