Question

An IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 90%confidence that the sample mean is within 8 IQ points of the true mean. Assume that o = 15 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation,

Answer 1

The required sample size is 13.5

No. This number of IQ test scores s a fairly small number.

Explanation:

We can calculate the sample size like this:

`n={\mleft({\frac{{{Z_(\alpha/2)}\sigma}}{E}}\mright)^2}`

Where,

n is the sample size.

Z is the standard normal variate.

α is the level of significance.

E is the margin of error.

σ is the population standard deviation

Replacing:

`\begin{gathered} n={({(1.96\cdot15)/(8)})^2} \\ n=13.5 \end{gathered}`

It is not a reasonable number, this number of IQ score is a fairly small number