Mathematics: 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.

To get 5, you will use the fraction 50/10, so since you have 57/10, you will need to subtract 7 from the 57. Have a nice day :D...

Assume that we want to estimate the mean iq score

harodkdc8463

15.01.2022

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.

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