Some quality-control experiments require destructive sampling (i.e., the test to determine whether the item is defective destroys the item) in order to measure some particular characteristic of the product. The cost of destructive sampling often dictates small samples. For example, suppose a manufacturer of printers for personal computers wishes to estimate the mean number of characters printed before the printhead fails. Suppose the printer manufacturer tests n = 15 randomly selected printheads and records the number of characters printed until failure for each. These 15 measurements (in millions of characters) are listed in Table 6.5, followed by an XLSTAT summary statistics printout in Figure 6.11.

a. Form a 99% confidence interval for the mean number of characters printed before the printhead fails. Interpret the result.

b. What assumption is required for the interval, part a, to be valid? Is it reasonably satisfied?

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Table 6.5 Number of Characters (in Millions) for n = 15 Printhead Tests 1.13 1.55 1.43 92 1.25 1.36 1.32 .85 1.07 1.48 1.29 1.20 1.33 1.18 1.22