Question

The gas mileages (in miles per gallon) of 28 randomly selected sports cars are listed in the accompanying table. Assume the mileages are not normally distributed. Use the standard normal distribution or the t-distribution to construct a 99% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. 囲Click the icon to view the sports car gas mileages. Let o be the population standard deviation and let n be the sample size. Which distribution should be used to construct the confidence interval? be used to construct the confidence interval, since choice below and, if necessary, fill in the answer box to complete your choice A t-distribution should The standard normal distribution should Neither distribution can r the t-distribution can be used to construct the interval. Interpret the results. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A With % confidence it can be said that the mean gas mileage of all sports cars in miles per gallon is between the interval's endpoints. O B. With % confidence it can be said that most sports cars in the population have gas mileages in miles per gallon) that are between the interval's endpoints. ° C. It can be said that % of all sports cars have a gas mileage (in miles per gallon) that is between the interval's endpoints. 。D. 9 of all random samples of 28 sports cars from the population of all sports cars will have a mean gas mileage in miles per gallon that is between the Click to select and enter your answer(s). Type an integer or a decimal. Do not round.) Type an integer or a decimal. Do not round.) (Type an integer or a decimal. Do not round.)

Answer 1

The gas mileage of 28 randomly selected sports cars are listed in the given table. The sample mean and the standard deviation is derived as follow: Mean = F x 574 = 20.5 11 n Standard deviation =- (x - 72 n-1=1 beſ(19–20.5)* +(29 – 20.5)² +...+(25 – 20.5)?] V 28-12 = 3.3278 Thus, the sample mean is r = 20.5 and the sample standard deviation is s = 3.3278. It is assumed that mileages are not normally distributed. Let o be the population standard deviation and let n be the sample size. The distribution that is used to construct a confidence interval is as follows: At-distribution should be used to construct the confidence interval, since o is unknown and the population is not normally distributed.

Using t-distribution, the 99 % confidence interval for the population mean (u) is constructed as follows: CI = F Šta/2.T Here, The level of significance is a = 0.01. The degrees of freedom are df =(n-1) = 27. Using t-table, the critical value is, ta/2,dr = 10.01,27 = 2.771 Thus, CI = x +ta/2,df vn 3.3278 = 20.5+ 2 = 20.5+1.7427 = (20.5 – 1.7427,20.5 +1.7427) = (18.7573, 22.2427) Thus, with 99% confidence, it can be said that the mean gas mileage of all sports cars ( in miles per gallons), that is, the population mean is between the interval (18.7573), 22.2427). So, the correct option is A.