302 CHAPTER 6 Confidence Intervals TRY IT YOURSELF 3 Use the data in Try It Yourself 1 and the result of Try It Yourself 2 to construct a 95% confidence interval for the mean number of hours spent per day on required athletic activities by all student-athletes in the conference. Answer: Page A40 The width of a confidence interval is 2E. Examine the formula for E to see why a larger sample size tends to give you a narrower confidence interval for the same level of confidence. Constructing a Confidence Interval Using Technology Use the data in Example 1 and technology to construct a 99% confidence interval for the mean number of hours spent per week on required athletic activities by all student-athletes in the conference. SOLUTION Minitab and StatCrunch each have features that allow you to construct a confidence interval. You can construct a confidence interval by entering the original data or by using the descriptive statistics. The original data were used to construct the confidence intervals shown below. From the displays, a 99% confidence interval for m is 118.9, 20.92. Note that this interval is rounded to the same number of decimal places as the sample mean. MINITAB One-Sample Z: Hours Descriptive Statistics N Mean StDev SE Mean 99% CI for μ 40 19.925 2.556 0.379 (18.948, 20.902) μ: population mean of Hours Known standard deviation: 2.4 STATCRUNCH One sample Z confidence interval: μ : Mean of variable Standard deviation = 2.4 99% confidence interval results: Variable n Sample Mean Std. Err. L. Limit U. Limit Hours 40 19.925 0.37947332 18.947542 20.902458 Interpretation With 99% confidence, you can say that the population mean number of hours spent per week on required athletic activities is between 18.9 and 20.9 hours. TRY IT YOURSELF 4 Use the data in Example 1 and technology to construct 75%, 85%, and 90% confidence intervals for the mean number of hours spent per week on required athletic activities by all student-athletes in the conference. How does the width of the confidence interval change as the level of confidence increases? Answer: Page A40 EXAMPLE 4 Tech Tip Here are instructions for constructing a confidence interval on a TI-84 Plus. First, either enter the original data into a list or enter the descriptive statistics. STAT Choose the TESTS menu. 7: ZInterval… Select the Data input option when you use the original data. Select the Stats input option when you use the descriptive statistics. In each case, enter the appropriate values, then select Calculate. Your results may differ slightly depending on the method you use. For Example 4, the original data were entered. x=19.925 Sx=2.555913204 n=40 (18.948,20.902) ZInterval
RkJQdWJsaXNoZXIy NjM5ODQ=