Question

Listed below are the top 10 salaries (in millions of dollars) of television personalities in a recent year.

38 36 35 27 15 13 12 10 9.6 8.4
Use the sample data to construct a 95% confidence interval for the population mean and correctly interpret your answer.

Answer 1

The correct answer is "(11.69, 29.11)".

Explanation:

Given:

`38 \ 36\ 35\ 27\ 15\ 13\ 12\ 10\ 9.6\ 8.4`

`n=10`

As per the question,

Mean,

`\bar x=20.40`

Standard deviation,

`s=12.17`

or,

`df=10-1`

`=9`

For 95% confidence interval,

`t^*=2.262`

hence,

The 95% confidence interval will be:

=
`\bar x \pm \ t^** (s)/(√(10) )`

By substituting the values, we get

=
`20.40 \pm 2.262* (12.17)/(√(10) )`

=
`(11.69, 29.11)`