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	102		88		7		94		106
2	108		102		8		81		88
3	101		97		9		77		76
4	96		105		10		58		59
5	99		81		11		95		62
6	81		82		12		104		102

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.)

b-2. Find the p-value.

• p-value 0.10
• 0.05 p-value < 0.10
• 0.025 p-value < 0.05
• 0.01 p-value < 0.025

• p-value < 0.01

c. At the 10% significance level, is there sufficient evidence to conclude that the safety program was effective?

• No, since we do not reject H₀.

• Yes, since we reject H₀.

• No, since we reject H₀.

• Yes, since we do not reject H₀.

Answer 1

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