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

396 Chapter 7 Confidence Intervals and Sample Size6. The best point estimate of the population mean isa. The sample meanb. The sample medianc. The sample moded. The sample midrange7. When the population standard deviation is unknown andthe sample size is less than 30, what table value shouldbe used in computing a confidence interval for a mean?a. zb. tc. Chi-squared. None of the aboveComplete the following statements with the best answer.8. A good estimator should be , , and. Unbiased, consistent, relatively efficient9. The maximum difference between the point estimate ofa parameter and the actual value of the parameter iscalled . Margin of error10. The statement “The average height of an adult maleis 5 feet 10 inches” is an example of a(n)estimate. Point11. The three confidence intervals used most often are the%, %, and %. 90; 95; 9912. Cost of Textbooks An irate student complained thatthe cost of textbooks was too high. He randomlysurveyed 36 other students and found that the meanamount of money spent for textbooks was $121.60. Ifthe standard deviation of the population was $6.36, findthe best point estimate and the 90% confidence intervalof the true mean. $121.60; $119.85 m $123.3513. Doctor Visit Costs An irate patient complainedthat the cost of a doctor’s visit was too high. Sherandomly surveyed 20 other patients and found thatthe mean amount of money they spent on eachdoctor’s visit was $44.80. The standard deviation ofthe sample was $3.53. Find a point estimate of thepopulation mean. Find the 95% confidence intervalof the population mean. Assume the variable isnormally distributed. $44.80; $43.15 m $46.4514. Weights of Minivans The average weight of 40randomly selected minivans was 4150 pounds. Thestandard deviation was 480 pounds. Find a point estimateof the population mean. Find the 99% confidence intervalof the true mean weight of the minivans.4150; 3954 m 434615. Ages of Insurance Representatives In a study of10 insurance sales representatives from a certain largecity, the average age of the group was 48.6 years and thestandard deviation was 4.1 years. Assume the variable isnormally distributed. Find the 95% confidence intervalof the population mean age of all insurance salesrepresentatives in that city. 45.7 m 51.516. Patients Treated in Hospital Emergency Rooms In ahospital, a sample of 8 weeks was selected, and it wasfound that an average of 438 patients was treated in theemergency room each week. The standard deviation was16. Find the 99% confidence interval of the true mean.Assume the variable is normally distributed. 418 m 45817. Burglaries For a certain urban area, it was found thatin a sample of 4 months, an average of 31 burglariesoccurred each month. The standard deviation was 4.Assume the variable is normally distributed. Find the90% confidence interval of the true mean number ofburglaries each month. 26 m 3618. Hours Spent Studying A university dean wishes toestimate the average number of hours that freshmen studyeach week. The standard deviation from a previousstudy is 2.6 hours. How large a sample must be selected ifhe wants to be 99% confident of finding whether the truemean differs from the sample mean by 0.5 hour? 18019. Money Spent on Road Repairs A researcher wishes toestimate within $300 the true average amount of moneya county spends on road repairs each year. If she wantsto be 90% confident, how large a sample is necessary?The standard deviation is known to be $900. 2520. Political Survey A political analyst found that 43% of300 Republican voters feel that the federal governmenthas too much power. Find the 95% confidence intervalof the population proportion of Republican voters whofeel this way. 0.374 p 0.48621. Emergency Room Accidents In a study of 150 accidentsthat required treatment in an emergency room, 36%involved children under 6 years of age. Find the 90%confidence interval of the true proportion of accidents thatinvolve children under the age of 6. 0.295 p 0.42522. Television Set Ownership A survey of 90 familiesshowed that 40 owned at least one television set. Find the95% confidence interval of the true proportion of familieswho own at least one television set. 0.342 p 0.54723. Skipping Lunch A nutritionist wishes to determine,within 3%, the true proportion of adults who do not eat anylunch. If he wishes to be 95% confident that his estimatecontains the population proportion, how large a samplewill be necessary? A previous study found that 15% of the125 people surveyed said they did not eat lunch. 54524. Novel Pages A sample of 25 novels has a standarddeviation of 9 pages. Find the 95% confidence intervalof the population standard deviation. 7 s 1325. Truck Safety Check Find the 90% confidence intervalfor the variance and standard deviation for the time ittakes a state police inspector to check a truck for safetyif a sample of 27 trucks has a standard deviation of6.8 minutes. Assume the variable is normallydistributed. 30.9 s 2 78.2; 5.6 s 8.826. Automobile Pollution A sample of 20 automobileshas a pollution by-product release standard deviation of2.3 ounces when 1 gallon of gasoline is used. Find the90% confidence interval of the population standarddeviation. 1.8 s 3.27–42