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. 95% of all taxi fares are between $20.52 and $22.48.
b. We are 95% confident that a randomly selected taxi fare will be between $20.52 and $22.48.
c. We can report that the average taxi fare between Logan Airport and downtown Boston will fall between $20.52 and $22.48.
d. With 95% confidence

Answer 1

Answer:

The correct option is C

Step-by-step explanation:

From the question we are told that

   The  sample mean is  $\= x =$$21.51

    The 95%  confidence level interval  is  [$ 20.52 , $22.48]

Generally the 95%  confidence level interval is mathematically represented as

      $\= x - MOE < \mu < \= x + MOE$

Where  MOE  is the margin of error which defines in percentage the amount by which the sample mean taxi fare(for the 7 taxi  ) will differ from the average taxi fare between Logan Airport and downtown Boston will fall between

Also  $\mu$ is the  average taxi fare between Logan Airport and downtown Boston

So we see that the this 95%  confidence level interval tells us  that  the average taxi fare between Logan Airport and downtown Boston will fall between $20.52 and $22.48.