Question

Case Study: Testing The Strength Of Cans

In the chapter opener, we discussed a method used to determine whether shipments of aluminum cans are strong enough to withstand the pressure of containing a carbonated beverage. Several cans are sampled from a shipment and tested to determine the pressure they can withstand. Based on this small sample, quality inspectors must estimate the proportion of cans that will fail at or below a certain threshold, which we will take to be 90 pounds per square inch.

The quality control inspectors want the proportion of defective cans to be no more than 0.001, or 1 in 1000. They test 10 cans, with the following results.

Can

1

2

3

4

5

6

7

8

9

10

Pressure at failure

95

96

98

99

99

100

101

101

103

104

None of the cans in the sample were defective; in other words, none of them failed at a pressure of 90 or less. The quality control inspectors want to use these data to estimate the proportion of defective cans in the shipment. If the estimate is to be no more than 0.001, or 1 in 1000, they will accept the shipment; otherwise, they will return it for a refund.

The following exercises will lead you through the process used by the quality control inspectors. Assume the failure pressures are normally distributed.

Question: Estimate the population mean μ with and the population standard deviation σ with s. In other words, assume that the data are a sample from a normal population with mean μ = and standard deviation σ = s. Under this assumption, what proportion of cans will fail at a pressure of 90 or less?

Answer 1

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