32. Scratch and dent An appliance manufacturer stockpiles wash- ers and dryers i

Question

32. Scratch and dent An appliance manufacturer stockpiles wash- ers and dryers in a large warehouse for shipment to retail stores. Sometimes in handling them the appliances get damaged. Even though the damage may be minor, the company must sell those machines at drastically reduced prices. The company goal is to keep the level of damaged machines below 2%. One day an in- spector randomly checks 60 washers and finds that 5 of them have scratches or dents. Is this strong evidence that the ware- house is failing to meet the company goal? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.

Explanation / Answer

First we summarize the data given to us as follows:

Sample size n = 60

Sample proportion p' = 5/60 = 0.083

The hypotheses to be tested in this case are as follows:

H0: p <= 0.02

Ha: p > 0.02

We calculate the standard error of the mean as shown below:

S' = ((p'*(1-p'))/n)^0.5 = ((0.083*(1-0.083))/60)^0.5 = 0.0356

Next we calculate the test statisti, as shown below:

t = (p'-0.02)/S' = (0.083-0.02)/0.0356 = 1.769

Degrees of freedom, df = n-1 = 59

So the p-value for this t-value is:

p = 0.041

Choosing a significance level of a = 0.05, we see that p < a

So we have to reject the null hypothesis.

Thus there is strong evidence that the warehouse is failing to meet the company goal.

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