Question

The population standard deviation for the age of Foothill College students is 15 years. If we want to be 95% confident that the sample mean age is within two years of the true population mean age of Foothill College students, how many randomly selected Foothill College students must be surveyed?

Answer 1

We need to survey at least 217 students.

Explanation:

We have that to find our
`\alpha` level, that is the subtraction of 1 by the confidence interval divided by 2. So:

`\alpha = (1-0.95)/(2) = 0.025`

Now, we have to find z in the Ztable as such z has a pvalue of
`1-\alpha`.

So it is z with a pvalue of
`1-0.025 = 0.975`, so
`z = 1.96`

Now, find the margin of error M as such

`M = z*(\sigma)/(√(n))`

In which
`\sigma` is the standard deviation of the population and n is the size of the sample.

How many randomly selected Foothill College students must be surveyed?

We need to survey at least n students.

n is found when
`\sigma = 15, M = 2`. So

`M = z*(\sigma)/(√(n))`

`2 = 1.96*(15)/(√(n))`

`2√(n) = 1.96*15`

`√(n) = (1.96*15)/(2)`

`(√(n))^(2) = ((1.96*15)/(2))^(2)`

`n = 216.09`

Rounding up

We need to survey at least 217 students.

Answer 2

n = 217

Explanation:

For 95% confidence, z = 1.96

Population standard deviation = 15

E = 2

Hence,

Number of Foothill College students required for survey

n = (\frac{1.96*15}{2})^2

n = 216.09

n = 217 [Rounded off to next whole number]