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 $22.31 and a 95% confidence interval of [$20.5051, $24.2091]. Which of the following statements is a valid explanation of the confidence interval.
A) 95% of all taxi fares are between $20.51 and $24.21.
B) We are 95% confident that a randomly selected taxi fare will be between $20.51 and $24.21.
C) The mean amount of a taxi fare is $22.31, 95% of the time.
D) We are 95% confident that the average taxi fare between Logan Airport and downtown Boston will fall between $20.51 and $24.21.

Question

Quizplus · Accepted Answer

The 95% confidence interval represents the range in which we would expect the true population mean to fall with 95% confidence. Therefore, option D is the only valid explanation. Option A is incorrect as we cannot make a statement about all taxi fares based on a sample. Option B is incorrect as we cannot be confident about an individual random sample. Option C is incorrect as we cannot say that the mean amount of a taxi fare is $22.31, 95% of the time, rather it is only true for this specific sample.

Suppose Taxi Fares from Logan Airport to Downtown Boston Is