Please create a Microsoft Word file with the answers to questions below. Question 1 THE DISK BRAKE CASE National Motors has equipped the ZX-900 with a new disk brake system. We define the stopping distance for a ZX-900 to be the distance (in feet) required to bring the automobile to a complete stop from a speed of 35 mph under normal driving conditions using this new brake system. In addition, we define i to be the mean stopping distance of all ZX 900s. One of the ZX-900's major competitors is advertised to achieve a mean stopping distance or 60 feet. National Motors would like to claim in a new advertising campaign that the ZX 900 achieves a shorter mean stopping distance. Suppose that National Motors randomly selects a sample of 81 ZX 900s. The company records the stopping distance of each automobile and calculates the mean and standard deviation of the sample of 81 stopping distances to be 57.8 ft and 6.02 f., respectively a Calculate a 95 percent confidence interval for . Can National Motors be 95 percent confident that is less than 60 ft? Explain. b Using the sample of 81 stopping distances as a preliminary sample, find the sample size necessary to make National Motors 95 percent confident that I is within a margin of error of one foot of H. Question 2 THE CIGARETTE ADVERTISEMENT CASE OS ModelAge A random sample of 50 perceived age estimates for a model in a cigarette advertisement showed that the sample mean and sample standard deviation were 26.22 years and 3.7432 years, respectively. a Use this sample to calculate a 95 percent confidence interval for the population mean age estimate for all viewers of the ad b Remembering that the cigarette industry requires that models must appear at least 25 years okl. does the confidence interval make us 95 percent confident that the population mean perceived age estimate is at least 25? Is the mean perceived age estimate much more than 25? Explain. Question 3 How safe are child car seats! Consumer Reports (May 2005) tested the safety of child car seats in 30 mph crashes. They found "slim safety margins" for some child car seats. Suppose that Consumer Reports simulates the safety of the market-leading child car seat. Their test consists of placing the maximum claimed weight in the car seat and simulating crashes at higher and higher miles per hour until a problem occurs. The following data identify the speed at which a problem with the car seat (such as the strap breaking, seat shell cracked, strap adjuster broke, detached from base, etc.) first appeared: 31.0.29.4.30.4.28.9 29.7. 30.1.32.3, 31.7.35.4, 29.1.31.2.30.2. Using the facts that the sample mean and sample standard deviation are 30.7833 and 1.7862, respectively, find a 95 percent confidence interval for the population mean speed at which a problem with the car seat first appears. Assume normality. Are we 95 percent confident that this population mean is at least 30 mplu? Explain. DS Car Seat
