Question: Technology Project

Using the pulse rates of females listed in Data Set 1 in Appendix \(\mathrm{B}\), we find that \(n=40, \bar{x}=76.3\), and \(s=12.5\). We will assume that these statistics are reasonably good estimates of the parameters for the population of all women. Conduct an experiment with the following steps:

1. Using STATDISK, Minitab, Excel, a TI-83/84 Plus calculator, or some other suitable technology, randomly generate 100 pulse rates from a normally distributed population having a mean of 76.3 and a standard deviation of 12.5.
2. Repeat Step i and generate a second sample of 100 values from a normally distributed population having a mean of 76.3 and a standard deviation of 12.5.
3. Generate a third sample of 100 values from a normally distributed population with a standard deviation of $12.5$, but use a mean of $81.3$ for this third sample.
4. Use the methods of this chapter to test the null hypothesis that the three samples come from populations having the same mean.
5. What do you conclude from Step 4? Given the way that the three samples were generated, we know that they come from populations with means that are not all equal. If Step 4 resulted in failure to reject the null hypothesis, what type of error was made (type I or type II)? Explain how correct application of a sound statistical procedure can result in such an error.

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