APU Math 302 Quiz 3 Problems

Question1of201.0PointsYou are told that a random sample of 150 people from Iowa has been given cholesterol tests, and 60of these people had levels over the safe count of 200. Construct a 95% confidence interval for thepopulation proportion of people in Iowa with cholesterol levels over 200. Place your LOWER limit,rounded to 3 decimal places, in the first blank . For example, .678 would be a legitimate entry. Placeyour UPPER limit, rounded to 3 decimal places, in the second blank . For example, .789 would be alegitimate entry.Question2of201.0PointsSenior management of a consulting services firm is concerned about a growing decline in the firmsweekly number of billable hours. The firm expects each professional employee to spend at least 40hours per week on work. In an effort to understand this problem better, management would like toestimate the standard deviation of the number of hours their employees spend on work-relatedactivities in a typical week. Rather than reviewing the records of all the firms full-time employees,the management randomly selected a sample of size 51 from the available frame. The sample meanand sample standard deviations were 48.5 and 7.5 hours, respectively.Construct a 90% confidence interval for the standard deviation of the number of hours this firmsemployees spend on work-related activities in a typical week.Place your LOWER limit, in hours, rounded to 1 decimal place, in the first blank. For example, 6.7would be a legitimate entry.Place your UPPER limit, in hours, rounded to 1 decimal place, in the second blank. For example, 12.3would be a legitimate entry.Question3of201.0PointsThe personnel department of a large corporation wants to estimate the family dental expenses of itsemployees to determine the feasibility of providing a dental insurance plan. A random sample of 12employees reveals the following family dental expenses (in dollars): 115, 370, 250, 593, 540, 225, 177,425, 318, 182, 275, and 228.Construct a 95% confidence interval estimate for the standard deviation of family dental expensesfor all employees of this corporation.Place your LOWER limit, in dollars rounded to 1 decimal place, in the first blank. Do not use a dollarsign, a comma, or any other stray mark. For example, 123.4 would be a legitimate entry.Place your UPPER limit, in dollars rounded to 1 decimal place, in the second blank. Do not use adollar sign, a comma, or any other stray mark. For example, 567.8 would be a legitimate entry.Question4of201.0PointsThe percent defective for parts produced by a manufacturing process is targeted at 4%. The processis monitored daily by taking samples of sizes n = 160 units. Suppose that todays sample contains 14defectives.How many units would have to be sampled to be 95% confident that you can estimate the fraction ofdefective parts within 2% (using the information from todays sample–that is using the resultthat)?Place your answer, as a whole number, in the blank. For example 567 would be a legitimate entry.Question5of201.0PointsYou are trying to estimate the average amount a family spends on food during a year. In the past, thestandard deviation of the amount a family has spent on food during a year has been$1200. Ifyou want to be 99% sure that you have estimated average family food expenditures within $60, howmany families do you need to survey? Place your answer, a whole number, in the blank . Forexample, 1234 would be a legitimate entry.Question6of201.0PointsAssume 50 random samples of the same sample size are taken from a population, and a 90%confidence interval is constructed from each sample. How many of the intervals would you expect tocontain the true population mean?Answer: Round your answer to a whole number value as necessary. For example, 37 would be alegitimate entry.Question7of201.0PointsThe manufacturer of a new compact car claims the miles per gallon (mpg) for the gasolineconsumption is mound-shaped and symmetric with a mean of 24.6 mpg and a standard deviation of11.2 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30cars will be greater than 27?Answer: Round your answer to 4 decimal places as necessary. For example, 0.1357 would be alegitimate entry.Part2of3Question8of201.0PointsWhen you calculate the sample size for a proportion, you use an estimate for the populationproportion; namelyA.0.50B.0.10C.0.01. A conservative value for n can be obtained by using= ______ .D.0.05Reset SelectionQuestion9of201.0PointsThe t- distribution for developing a confidence interval for a mean has _____ degrees of freedom.A.n1B.n+1C.n2D.nReset SelectionQuestion10of201.0PointsA food snack manufacturer samples 15 bags of pretzels off the assembly line and weighed theircontents. If the sample mean is 10.0 and the sample standard deviation is 0.15, find the 95%confidence interval estimate for the true mean.A.(9.96,10.04)B.(9.68,10.32)C.(9.97,10.80)D.(9.92,10.08)Reset SelectionQuestion11of201.0PointsThe average gas mileage of a certain model car is 26 miles per gallon. If the gas mileages arenormally distributed with a standard deviation of 1.3, find the probability that a randomly selectedcar of this model has a gas mileage between 25.8 and 26.3 miles per gallon.A.0.15B.0.85C.0.70D.0.30Reset SelectionQuestion12of20Compute1.0Pointswhere t20 has a t-distribution with 20 degrees of freedom.A.0.5334B.0.6466C.0.8233D.0.1767Reset SelectionQuestion13of201.0PointsIf you are constructing a confidence interval for a single mean, the confidence intervalwill___________ with an increase in the sample size.A.staythesameB.increaseC.increaseordecrease,dependingonthesampledataD.decreaseReset SelectionQuestion14of20Confidence intervals are a function of which of the following three things?1.0PointsA.Thesample,thevariableofinterest,andthedegreesoffreedomB.Thesamplingdistribution,theconfidencelevel,andthedegreesoffreedomC.Thedatainthesample,theconfidencelevel,andthesamplesizeD.Thepopulation,thesample,andthestandarddeviationReset SelectionQuestion15of201.0PointsIn order to be accepted into a top university, applicants must score within the top 5% on the SATexam. Given that SAT test scores are normally distributed with a mean of 1000 and a standarddeviation of 200, what is the lowest possible score a student needs to qualify for acceptance intothe university?A.1330B.1400C.1250D.1100Reset SelectionQuestion16of201.0PointsThe upper limit of the 90% confidence interval for the population proportion p, given that n = 100;and= 0.20 isA.0.2658B.0.7342C.0.5316D.0.4684Reset SelectionQuestion17of201.0PointsFind the 95% confidence interval for the standard deviation of the lengths of pipes if a sample of 26pipes has a standard deviation of 10 inches.A.14.0<B.7.8<<16.0<13.8C.74.0<<126.0D.60.8<<190.5Reset SelectionQuestion18of201.0PointsA previous study of nickels showed that the standard deviation of the weight of nickels is 150milligrams. How many nickels does a coin counter manufacturer need to weigh so that she can be98% confident that her sample mean is within 25 milligrams of the true average weight of a nickel?A.36B.196C.239D.139Reset SelectionPart3of3Question19of201.0PointsThe 95% confidence interval for the population meanpopulation standard deviationTrue= 7, is, given that the sample size n = 49 and the.FalseReset SelectionQuestion20of201.0PointsThe upper limit of the 90% confidence interval for the population proportion p, given that n = 100;and= 0.20 is 0.2341.TrueFalse