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# Hypothesis testing questions

An industry safety program was recently instituted in the pharmaceutical industry. The weekly average losses (averaged over 1 month) in man-hours due to accidents in 10 similar plants before and after the program are as follows:

PLANT BEFORE AFTER
1 30.5 23.0
2 18.5 21.0
3 24.5 22.0
4 32.0 28.5
5 16.0 14.5
6 15.0 15.5
7 23.5 24.5
8 25.5 21.0
9 28.0 23.5
10 18.0 16.5

Determine, at the 5% level of significance (i.e., Alpha = 0.05), whether the safety program has been proven to be effective.

2.
A public health official claims that the mean home water use is 350 gallons per day. To verify this claim, a study of 20 randomly selected homes was investigated and the daily water uses of these 20 homes (gallons per day) are: [340, 356, 332, 362, 318, 344, 386, 402, 322, 360, 362, 354, 340, 372, 338, 375, 364, 355, 324, 370]. Do the data contradict the official's claim?
Use Alpha = 0.10. Hint: check the normailty of the data set.

3.
If a shipment of N = 50 steel rods is to be used in the construction of a bridge. The lot must be checked to ensure that the breaking strength of the rods meets specifications. The lot will be rejected if it appears that more than 10% of the rods fail to meet specifications. We are testing

Ho: Theta = 0.1 = Thetao (lot is acceptable)
H1: Theta>= 0.1 (lot is unacceptable)

Where Theta = D/N. Since testing a rod requires that it be broken, we cannot test each rod in the lot. Instead, we select randomly a sample of size n = 5, and we agree to reject the lot if more than one rod is found to be defective. What is the producer's risk?

#### Solution Summary

This posting contains 3 questions on Hypothesis testing

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