# Solved (Free): Number skills of young men. Suppose that scores of men aged 21 to 25 years on the quantitative part of the National Assessment of Education Progress

#### ByDr. Raju Chaudhari

Apr 16, 2021

Number skills of young men. Suppose that scores of men aged 21 to 25 years on the quantitative part of the National Assessment of Education Progress (NAEP) test follow a Normal distribution with standard deviation $\sigma= 60$. You want to estimate the mean score within $\pm$ 10 with 90% confidence. How large an SRS of scores must you choose?

#### Solution

Given that the sample standard deviation $s =60$, margin of error $E =10$. The confidence coefficient is $1-\alpha=0.9$. Thus $\alpha = 0.1$.

The critical value of $Z$ is $z=Z_{\alpha/2} = 1.64$.

The minimum sample size required to estimate the mean is

 \begin{aligned} n &= \bigg(\frac{z* s}{E}\bigg)^2\\ & = \bigg(\frac{1.64*60}{10}\bigg)^2\\ & =96.8256\\ &\approx 97. \end{aligned}
Thus, the sample of size $n=97$ will ensure that the $90$% confidence interval for the mean will have a margin of error $10$.