p-value Approach

Null & Alternative Hypothesis

Significance Level Of the Test

a

a

a

Test Statistics

p-value

Table VI with d.f.=n-1

Table VI with d.f.=n-1

Table VI with

d.f.=n-1

Decision

Test
of hypothesis on mean by using summary statistics

ACTIVITY

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 characteristics of the product. The cost of desctructive sampling often dictates small samples. Suppose a manufacturer of printers for personal computers wishes to estimate the mean number of characters printed before the printhead fails. The printer manufacturer tests n = 15 printheads and records the number of characters printed until failure for each. Suppose that the competitor's printers has a mean of 1.30 (in millions) for the number of characters printed before the printhead fails.These 15 measurements (in millions of characters) are listed in the following table. Suppose that the competitor's printers has a mean of 1.30 (in millions) for the number of characters printed before the printhead fails

Number of Characters (in Millions) for n = 15 Printhead Tests
1.33 1.55 1.43 0.92 1.25 1.36 1.32 0.85 1.07 1.48 1.20 1.33 1.18 1.22 1.29

a. Test the hypothesis that mean number of characters printed before the printhead fails for this manufacturer is different than its competitor. Use the significance level 0.05.

 

The output will include: Sample size, Mean, Standard deviation, a 95% confidence interval for the population mean, and the result of the test.

b. Test the hypothesis that mean number of characters printed before the printhead fails for this manufacturer is less than its competitor. Use the significance level 0.05.

The output will include: Sample size, Mean, Standard deviation, one-sided 95% confidence interval for the population mean, and the result of the test.

c. The manufacturer advertises that mean number of characters printed before the printhead fails for their printer is 1.4 (in million). What would be your response?

Note the p-value of this test and respond to the question.