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

Answer:

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

Step-by-step explanation:

The give values are:

Mean,

= $167

Standard deviation,

$\sigma$ = $40

Number of commuters,

n = 100

Now,

⇒ $SE=\frac{\sigma}{\sqrt{n} }$

On putting the given values, we get

⇒       $=\frac{40}{\sqrt{100} }$

⇒       $=\frac{40}{10}$

⇒       $=4$

By using the 2 SE rule of thumb, we get

= $(167 - 2\times 4)$

= $167-8$

= $159$ ($)

Or,

= $(167 + 2\times 4)$

= $167+8$

= $175$ ($)

i.e,

$159 and $175