Question

Assume that we want to estimate the mean IQ score for the population of statistics professors. How many statistics professors must be randomly selected for IQ tests if we want 95% confidence that the sample mean is within 2 IQ points of the population mean? Assume that the standard deviation of the IQ of statistics professors is
σ
= 15.

Answer 1

Answer:

You should select at least 216 statistics professors.

Step-by-step explanation:

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

$\alpha = \frac{1-0.95}{2} = 0.025$

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 M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

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

In this problem, we have that:

$M = 2, \sigma = 15$

$M = z*\frac{\sigma}{\sqrt{n}}$

$2 = 1.96*\frac{15}{\sqrt{n}}$

$2\sqrt{n} = 29.4$

$\sqrt{n} = 14.7$

$\sqrt{n}^{2} = (14.7)^{2}$

$n = 216$

You should select at least 216 statistics teachers.