Bluman A.G. Elementary Statistics- A Step By Step Approach

Chapter Quiz 395StatisticsTodayWould You Change the Channel?—RevisitedThe estimates given in the survey are point estimates. However, since the margin of error isstated to be 3 percentage points, an interval estimate can easily be obtained. For example, if45% of the people changed the channel, then the confidence interval of the true percentages ofpeople who changed channels would be 42% p 48%. The article fails to state whether a90%, 95%, or some other percentage was used for the confidence interval.Using the formula given in Section 7–3, a minimum sample size of 1068 would be neededto obtain a 95% confidence interval for p, as shown. Use pˆ and qˆ as 0.5, since no value isknown for pˆ .n pˆqˆ a2zE 2 (0.5)(0.5) 1.96 1067.10.03 2 1068Data AnalysisThe Data Bank is found in Appendix D, or on theWorld Wide Web by following links fromwww.mhhe.com/math/stat/bluman/.1. From the Data Bank choose a variable, find the mean,and construct the 95 and 99% confidence intervals of thepopulation mean. Use a sample of at least 30 subjects.Find the mean of the population, and determine whetherit falls within the confidence interval.2. Repeat Exercise 1, using a different variable and asample of 15.3. Repeat Exercise 1, using a proportion. For example,construct a confidence interval for the proportion ofindividuals who did not complete high school.4. From Data Set III in Appendix D, select a sample of30 values and construct the 95 and 99% confidenceintervals of the mean length in miles of majorNorth American rivers. Find the mean of all thevalues, and determine if the confidence intervalscontain the mean.5. From Data Set VI in Appendix D, select a sample of 20values and find the 90% confidence interval of the meanof the number of acres. Find the mean of all the values,and determine if the confidence interval contains themean.6. Select a random sample of 20 of the record hightemperatures in the United States, found in Data Set I inAppendix D. Find the proportion of temperatures below110°. Construct a 95% confidence interval for thisproportion. Then find the true proportion of temperaturesbelow 110°, using all the data. Is the true proportioncontained in the confidence interval? Explain.Chapter QuizDetermine whether each statement is true or false. If thestatement is false, explain why.1. Interval estimates are preferred over point estimatessince a confidence level can be specified. True2. For a specific confidence interval, the larger the samplesize, the smaller the margin of error will be. True3. An estimator is consistent if as the sample sizedecreases, the value of the estimator approaches thevalue of the parameter estimated. False4. To determine the sample size needed to estimate aparameter, you must know the margin of error. TrueSelect the best answer.5. When a 99% confidence interval is calculated instead ofa 95% confidence interval with n being the same, themargin of error will bea. Smallerb. Largerc. The samed. It cannot be determined.7–41