Question

Suppose taxi fares from Logan Airport to downtown Boston is known to be normally distributed and a sample of seven taxi fares produces a mean fare of $21.51 and a 95% confidence interval of [$20.52, $22.48]. Which of the following statements is a valid interpretation of the confidence interval?

a. we are 95% confident that a randomly selected taxi fare will be between $2051 and $2421.
b. 95% of all taxi fares are between $2051 and $2421.
c. We are 95% confident that the average tau fare between Logan Airport and downtown Boston will fall between $2051 and $2421.
d. The mean amount of a taxi fare is $22.31, 95% of the time.

Answer 1

c. We are 95% confident that the average taxi fare between Logan Airport and downtown Boston will fall between $20.51 and $24.21.

Explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

95% confidence interval of [$20.52, $22.48].

We can be 95% sure that the true mean amount of taxis fares in downtown Boston is in this interval, and thus, the correct answer is given by option C.