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 (in millions of characters)

a. Find a 95% confidence interval by following the steps given below:

• 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.

The output will include: Sample size, Mean, and Standard deviation followed by 95% confidence interval for the population mean.

b. Find a 99% confidence interval by following the steps given below:

• 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.
• Step 7: Click on the "Options" button on the upper right hand side of the window.
• Step 8: Change only Alpha from 5.0 to 1.0.
• Step 9: Click on the "OK" button.

The output will include: Sample size, Mean, and Standard deviation followed by 99% confidence interval for the population mean.

c. Compare the length of the confidence intervals that you have found in a and b. Which one is shorter?