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 $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.

Answer 1

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

Explanation:

The Confidence interval allows one to speculate between which values the average of a population will be. In a 95% confidence interval, this means that we are 95% certain that the average value of a variable will be between the higher and lower limits set by the interval.

The 95% confidence interval here has an upper limit of  $24.2091 and a lower limit of $20.5051 for taxi fares from Logan Airport to downtown Boston. This means that with a 95% certainty, the taxi charge from Logan Airport to downtown Boston will be between these 2 charges so you can expect to pay an amount between them.