7-2 Estimating a Population Mean 341 Statistical Literacy and Critical Thinking In Exercises 1–4, refer to the accompanying screen display that results from a simple random sample of times (minutes) between eruptions of the Old Faithful geyser. The confidence level of 95% was used. 7-2 Basic Skills and Concepts TI-83, 84 Plus 1.Old Faithful Refer to the accompanying screen display. a. Express the confidence interval in the format that uses the “less than” symbol. Round the confidence interval limits given that the original times are all rounded to one decimal place. b. Identify the best point estimate of m and the margin of error. 2.Degrees of Freedom a. What is the number of degrees of freedom that should be used for finding the critical value ta>2? b. Find the critical value ta>2 corresponding to a 95% confidence level. c. Give a brief general description of the number of degrees of freedom. 3.Interpreting a Confidence Interval The results in the screen display are based on a 95% confidence level. Write a statement that correctly interprets the confidence interval. 4. Requirements a. What are the requirements for using the methods of this section to construct a confidence interval estimate of a population mean? b. What does it mean when we say that the confidence interval methods of this section are robust against departures from normality? c. Does the sample used for the accompanying screen display satisfy the requirements for constructing a confidence interval estimate of the population mean m? Explain. In Exercises 5–8, (a) identify the critical value tA,2 used for finding the margin of error, (b) find the margin of error, (c) find the confidence interval estimate of m, and (d) write a brief statement that interprets the confidence interval. 5.Birth Weights Here are summary statistics for randomly selected weights of newborn girls: n = 36, x = 3150.0g, s = 695.5g (based on Data Set 6 “Births” in Appendix B). Use a confidence level of 95%. 6.Hershey Kisses Here are summary statistics for randomly selected weights of Hershey Kisses: n = 32, x = 4.5210g, s = 0.1077g (based on a sample from Data Set 38 “Candies” in Appendix B). Use a confidence level of 99%. 7.Pepsi Weights Here are summary statistics for the weights of Pepsi in randomly selected cans: n = 36, x = 0.82410 lb, s = 0.00570lb (based on Data Set 37 “Cola Weights and Volumes” in Appendix B). Use a confidence level of 99%. 8.Airport Data Speeds Here are summary statistics for the phone data speeds of Verizon in different airports: n = 38, x = 18.86 Mbps, s = 15.66Mbps (based on a sample from Data Set 34 “Airport Data Speeds” in Appendix B). Use a confidence level of 95%. Confidence Intervals. In Exercises 9–20, construct the confidence interval estimate of the mean. 9. Mean Body Temperature Data Set 5 “Body Temperatures” in Appendix B includes a sample of 106 body temperatures having a mean of 98.20°F and a standard deviation of 0.62°F. Construct a 95% confidence interval estimate of the mean body temperature for the entire population. What does the result suggest about the common belief that 98.6°F is the mean body temperature?
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