Question

the gas mileages (in miles per gallon) of 27 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 95% confidence interval for the population mean. justify your decision. if neither distribution can be used, explain why. interpret the results
click the icon to view the sports car gas mileages.
b. neither the standard normal distribution nor 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.
a. it can be said that % of all sports cars have a gas mileage (in miles per gallon) that is between the intervals endpoints
(type an integer or a decimal. do not round.)
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 intervals endpoints
(type an integer or a decimal. do not round.)
c. % of all random samples of 27 sports cars from the population of all sports cars will have a mean gas mileage (in miles per gallon) that is between the intervals endpoints
(type an integer or a decimal. do not round.)
d. with % confidence, it can be said that the mean gas mileage of all sports cars (in miles per gallon) is between the intervals endpoints
(type an integer or a decimal. do not round.)
e. neither the standard normal distribution nor the t - distribution can be used to construct the interval.

Explanation:

Since neither the standard normal distribution nor the t - distribution can be used (as given in the problem statement), we cannot construct a confidence interval in the traditional parametric way. When interpreting confidence intervals for the population mean (in cases where they can be constructed), the correct interpretation is that with a certain percentage of confidence (e.g., 95%), we can say that the population mean lies within the interval. But here, because the distributions are not applicable, we refer to the option that acknowledges the inability to use the distributions.

Answer:

E. Neither the standard normal distribution nor the t - distribution can be used to construct the interval.