318 Confidence Intervals for a Mean 6.2 ACTIVITY APPLET You can find the interactive applet for this activity at MyLab Statistics. 318 CHAPTER 6 Confidence Intervals The Comparing confidence intervals for a mean applet allows you to visually investigate confidence intervals for a population mean. You can specify the Distribution (Normal or Right skewed), Sample size, population Mean, population Std. Dev., and Interval type (T or Z). When you click Update applet, 100 separate samples of the specified size are selected from a population with these population parameters. For each of the 100 samples, a 95% Z confidence interval (known standard deviation) or a 95% T confidence interval (unknown standard deviation) is displayed in green when it includes the mean, or in red when it does not include the mean. Each time you click Update applet you get a new simulation. The level of confidence used for the intervals can be changed within the applet itself by updating the CI level input. You can generate additional samples with the given confidence interval by clicking 100 intervals or 1000 intervals. The cumulative number of intervals that contain the population mean is also shown. Press Reset to clear existing results and start a new simulation. EXPLORE Step 1 Specify a Distribution. Step 2 Specify a Sample size. Step 3 Specify a value for the Mean. Step 4 Specify a value for the Std. Dev. Step 5 Click Update Applet, 100 intervals, or 1000 intervals to generate confidence intervals. DRAW CONCLUSIONS 1. Set Distribution = Normal, Sample size = 30, Mean = 25, and Std. Dev. = 5. At the 95% confidence level, compare the numbers containing m for 1000 Z confidence intervals and 1000 T confidence intervals. Is this what you would expect? Explain. 2. In a random sample of 24 high school students, the mean number of hours of sleep per night during the school week was 7.26 hours and the standard deviation was 1.19 hours. Assume the sleep times are normally distributed. Use a sample size of 10 to generate 500 Z confidence intervals and 500 T confidence intervals. At the 95% confidence level, compare the numbers containing m for the two distributions. Which type of confidence interval should you use for the mean number of hours of sleep? APPLET Confidence intervals for a mean: Normal population (μ=50, б=10)Type=T 100 intervals Sample size 1000 intervals Update Applet Reset Info Sort graph Sample size: Interval type: Mean: 100 Distribution: Normal 100 < 50 Std. dev.: 10 Intervals 1 to 100 20 30 70 60 50 40 Intervals CI Level 0.95 94 100 74 Containing μ Total Prop. contain 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
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