If you have been given or calculated the sample mean and sample standard deviation together with the sample size you can use the Statlets window presented below.

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. These 15 measurements yield a mean of 1.24 and a standard deviation of 0.19 9in millions of characters). Suppose that the competitor's printers has a mean of 1.30 (in millions) for the number of characters printed before the printhead fails.

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.

• Step 1: Make sure that "Input" menu option is selected.
• Step 2: Type "Number" in the "Data label" box.
• Step 3: Type "15" in the "Sample size" box.
• Step 4: Type "1.24" in the "Sample mean" box.
• Step 5: Type "0.19" in the "Sample standard deviation" box.
• Step 6: Select the "t test" from menu options.Caution: Do not use the output yet.
• Step 7: Click on the "Options" button on the upper right hand side of the window.
• Step 8: On the window that pops up, type the value of the mean specified in you null hypothesis. That is 1.3 in this case.
• Step 9: Select your alternative hypothesis. For this question the alternative hypothesis is two sided (we are interested whether the mean is different or not). Therefore select "Not equal".
• Step 10: Type the significance level of the test. In this case it is "5.0"
• Step 11: Click on the "OK" button.

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.

• Step 1: Make sure that "Input" menu option is selected.
• Step 2: Type "Number" in the "Data label" box.
• Step 3: Type "15" in the "Sample size" box.
• Step 4: Type "1.24" in the "Sample mean" box.
• Step 5: Type "0.19" in the "Sample standard deviation" box.
• Step 6: Select the "t test" from menu options.Caution: Do not use the output yet.
• Step 7: Click on the "Options" button on the upper right hand side of the window.
• Step 8: On the window that pops up, type the value of the mean specified in you null hypothesis. That is 1.3 in this case.
• Step 9: Select your alternative hypothesis. For this question the alternative hypothesis is one sided (we are interested whether the mean is less). Therefore select "Less than".
• Step 10: Type the significance level of the test. In this case it is "5.0"
• Step 11: Click on the "OK" button.

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?

• Step 1: Make sure that "Input" menu option is selected.
• Step 2: Type "Number" in the "Data label" box.
• Step 3: Type "15" in the "Sample size" box.
• Step 4: Type "1.24" in the "Sample mean" box.
• Step 5: Type "0.19" in the "Sample standard deviation" box.
• Step 6: Select the "t test" from menu options.Caution: Do not use the output yet.
• Step 7: Click on the "Options" button on the upper right hand side of the window.
• Step 8: On the window that pops up, type the value of the mean specified in you null hypothesis. That is 1.4 in this case.
• Step 9: Select your alternative hypothesis. For this question the alternative hypothesis is one sided (we are interested whether the mean is less). Therefore select "Less than".
• Step 10: Type the significance level of the test. In this case it is "5.0"
• Step 11: Click on the "OK" button.

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