Question

A public relations officer of William Paterson University wants to estimate the mean IQ of the university students. If she wants to be 99% confident that her sample mean is off by no more than 3 points, how many students she has to test in order to come up with a valid estimation? A recent study shows that IQ of New Jersey students has standard deviation of 15 points.

Answer 1

She has to test 166 students in order to come up with a valid estimation.

Explanation:

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

`\alpha = (1-0.99)/(2) = 0.005`

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
`1-0.005 = 0.995`, so
`z = 2.575`

Now, find 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.

If she wants to be 99% confident that her sample mean is off by no more than 3 points, how many students she has to test in order to come up with a valid estimation?

She test have at least n students, in which n is found
`M = 3, \sigma = 15`. So

`M = z*(\sigma)/(√(n))`

`3 = 2.575*(15)/(√(n))`

`√(n) = (2.575*15)/(3)`

`√(n) = 12.875`

`(√(n))^(2) = (12.875)^(2)`

`n = 165.7`

Rouding up

She has to test 166 students in order to come up with a valid estimation.