Question

Suppose you asked 100 commuters how much they spend each year and obtained a mean of $167 spent on transportation and a standard deviation of $40. Using the 2 SE rule of thumb, calculate a 95% confidence interval for the mean and select the values that come closest to those that would fill the spaces in the following interpretation: we can be 95% confident that the mean amount of money spent on transportation lies between _____ and _____ .

Answer 1

The correct answer is "$159 and $175".

Explanation:

The give values are:

Mean,

= $167

Standard deviation,

`\sigma` = $40

Number of commuters,

n = 100

Now,

⇒
`SE=(\sigma)/(√(n) )`

On putting the given values, we get

⇒
`=(40)/(√(100) )`

⇒
`=(40)/(10)`

⇒
`=4`

By using the 2 SE rule of thumb, we get

=
`$(167 - 2* 4)`

=
`167-8`

=
`159` ($)

Or,

=
`(167 + 2* 4)`

=
`167+8`

=
`175` ($)

i.e,

$159 and $175