91影视

Replacement

Why does the bootstrap method require sampling with replacement? What would happen if we used the methods of this section but sampled without replacement?

In Exercises 1鈥�3, refer to the accompanying screen display that results from the Verizon airport data speeds (Mbps) from Data Set 32 鈥淎irport Data Speeds鈥� in Appendix B. The confidence level of 95% was used

Airport Data Speeds Refer to the accompanying screen display.

a. Express the con铿乨ence interval in the format that uses the 鈥渓ess than鈥� symbol. Given that the original listed data use one decimal place, round the con铿乨ence interval limits accordingly.

b. Identify the best point estimate of and the margin of error.

c. In constructing the con铿乨ence interval estimate of , why is it not necessary to con铿乺m that the sample data appear to be from a population with a normal distribution?

Flight Arrivals. Listed below are the arrival delay times (min) of randomly selected American Airlines flights that departed from JFK in New York bound for LAX in Los Angeles. Negative values correspond to flights that arrived early and ahead of the scheduled arrival time. Use these values for Exercises 1鈥�4.

-30 -23 14 -21 -32 11 -23 28 103 -19 -5 -46

Statistics Find the mean, median, standard deviation, and range. Are the results statistics or parameters?

Critical Thinking: What does the survey tell us? Surveys have become an integral part of our lives. Because it is so important that every citizen has the ability to interpret survey results, surveys are the focus of this project. The Pew Research Center recently conducted a survey of 1007 U.S. adults and found that 85% of those surveyed know what Twitter is.

Analyzing the Data

Use the survey results to construct a 95% confidence interval estimate of the percentage of all adults who know what Twitter is.

Brain Volume Using all of the brain volumes listed in Data Set 8 鈥淚Q and Brain Size鈥�, we get this 95% confidence interval estimate: 9027.8< $蟽$< 33,299.8, and the units of measurement are ${\left(c{m}^3\right)}^2$. Identify the corresponding confidence interval estimate of $蟽$ and include the appropriate units. Given that the original values are whole numbers, round the limits using the round-off rule given in this section. Write a statement that correctly interprets the confidence interval estimate of $蟽$.

Celebrities and the Law Here is a 95% confidence interval estimate of the proportion of adults who say that the law goes easy on celebrities: 0.692 <p< 0.748 (based on data from a Rasmussen Reports survey). What is the best point estimate of the proportion of adults in the population who say that the law goes easy on celebrities?

Online News In a Harris poll of 2036 adults, 40% said that they prefer to get their news online. Construct a 95% confidence interval estimate of the percentageof all adults who say that they prefer to get their news online. Can we safely say that fewer than 50% of adults prefer to get their news online?

Birth Weights of Boys Use these summary statistics for birth weights of 195 boys: $\stackrel{\mathbf{炉}}{\mathbf{x}}鈥�\mathbf{=}\mathbf{32}\mathbf{.}\mathbf{7}鈥�\mathbf{hg}$,$\mathbf{s}鈥�\mathbf{=}\mathbf{6}\mathbf{.}\mathbf{6}鈥�\mathbf{hg}$. (based on Data Set 4 鈥淏irths鈥� in Appendix B). Use a 95% confidencelevel. Are the results very different from those found in Exercise 9? Does it appear that boys and girls have very different birth weights?

In Exercises 9鈥�16, assume that each sample is a simplerandom sample obtained from a population with a normal distribution.

Atkins Weight Loss Program In a test of weight loss programs, 40 adults used the Atkins weight loss program. After 12 months, their mean weightlosswas found to be 2.1 lb, with a standard deviation of 4.8 lb. Construct a 90% confidence interval estimate of the standard deviation of the weight loss for all such subjects. Does the confidence interval give us informationabout the effectiveness of the diet?

Formats of Confidence Intervals.

In Exercises 9鈥�12, express the confidence interval using the indicated format. (The confidence intervals are based on the proportions of red, orange, yellow, and blue M&Ms in Data Set 27 鈥淢&M Weights鈥� in Appendix B.)

Orange M&Ms Express 0.179 < p < 0.321 in the form of $\hat{p}卤E$.