Question

Suppose taxi fares from Logan Airport to downtown Boston is known to be normally distributed and a sample of seven taxi fares produ confidence interval

we are 95% confident that a randomly selected taxi fare will be between S2051 and S2421

95% of all taxi fares are between S2051 and S2421

We are 95% confident that the average tau fare between Logan Airport and downtown Boston will fall between S2051 and S2421.

The mean amount of a taxi fare is S22.31, 95% of the time

Answer 1

Explanation:

Hello!

The variable of the study is

X: taxi fare from Logan Airport to downtown Boston.

This variable has a normal distribution

Suppose a sample of 7 taxi fares was taken and a 95%CI for the population mean was calculated obtaining:

$[20.51; 24.21]

The confidence level is a way of estimating the value of a population parameter of interest just like the point estimation. The difference is that instead of obtaining one value that may or may not be close to the true value of the parameter you obtain the range of values the parameter may take with a certain level of confidence.

The confidence level of an interval is the probability under which it is built. This probability indicates that if they build 100 confidence intervals, we expect 95 to contain the value of the parameter of interest we are trying to estimate.

As mentioned before in this case the parameter of interest is:

μ: population mean of taxi fares from Logan Airport to downtown Boston

And the 95% CI can be interpreted as:

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

I hope this helps!