Question

The mean gas mileage of 14 randomly selected cars is 19.5 mpg and the standard deviation...

The mean gas mileage of 14 randomly selected cars is 19.5 mpg and the standard deviation is 3.4 mpg. The mileages(i.e are not normally distributed. Give 2 reasons why neither the standard normally distributed. (i.e the z-distribution) nor the t-distribution, can be used to construct a 90% confidence interval for the population mean.

Solution:

The two reasons that explain why we can neither use the standard normal distribution nor the t-distribution for constructing the 90% confidence interval for the population mean are:

1. Non-Normal population: The population of mileages mentioned in the question is not normal, therefore, we can not use any of these two methods for constructing the confidence interval for the population mean.

2. Small sample size: The sample size used in the given problem is 14, which according to the central limit theorem is not large enough to be used for constructing the confidence interval for the population mean using any of the methods mentioned in the given question.

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