8.2A Understanding Confidence Intervals Activity Name: The following activity is designed to help you better understand the underlying reasoning behind the interpretation of confidence intervals. In particular, you will gain a deeper understanding of why we say that we are "95% confident that the population mean is contained in the interval." In this activity, you will identify how often a 95% confidence interval does actually include the true population mean p. To begin the activity, open: The Confidence Interval Applet Confidence Intervals digitalfirst.bfwpub.com When the applet loads, you will see a Normal population distribution along with a sampling distribution. The green line represents the true population mean p. A. Make sure the Confidence Level C is set at 95 and the sample size n is 20. B. Press the SAMPLE button to simulate selecting 1 sample from the population. Under the graph you will see the sampled values as yellow dots. . The red dot is the sample mean x. . The red line is the confidence interval. 1. Did the confidence interval for the first sample contain the population mean p? Yes No 2. Describe where the population mean p is compared to the confidence interval. C. Notice that the applet will be keeping track of your "Hit Percentage" which will tell you what percent of the confidence intervals contain the population mean . D. Press the SAMPLE button again to collect your 2nd sample.3. Was your second sample mean x the same value as your first sample mean? Yes No 4. Explain why our sample means are usually different. 5. Does your second confidence interval contain the population mean p? Yes No 6. After two samples, what is your hit percentage: E. Press SAMPLE 25 to take 25 samples at once. 7. How many of these 25 samples do not contain the population mean p? 8. Would you say your results in #7 are surprisingly high, surprisingly low, or about as expected? Explain. F. Press SAMPLE 25 until you have taken a total of about 1000 samples. 9. Now what is your hit percentage? 10. When we say that we are "95% confident", we are saying that we think something will happen 95% of the time. When we make a 95% Confidence Interval, what do we think is going to happen 95% of the time