Q.9 - The Practice of Statistics for AP

Question

 Good wood? A lab supply company sells pieces of Douglas fir $4$ inches long and $1.5$ inches square for force experiments in science classes. From experience, the strength of these pieces of wood follows a Normal distribution with standard deviation $3000$ pounds. You want to estimate the mean load needed to pull apart these pieces of wood to within $1000$ pounds with $95\%$ confidence. How large a sample is needed? Show your work.

- Understand how the margin of error of a confidence interval changes with the sample size and the level of confidence $C$.

Step-by-Step Solution

Answer

The sample size is $35$

Step-1 Given Information

Given in the question that ,

Margin of error$\left(E\right)=1000$

Standard deviation$\left(\sigma \right)=3000$

Confidence level$=95\%$ we have to find How large a sample is needed.

Step-2 Explanation

The  value of   $z\frac{\alpha }{2}$corresponding  to  $95\%$ confidence level $1.96$ which is obtained from standard normal table.

the sample size can be calculated as follows:

$Sample size \left(n\right)={\left(\frac{z{\displaystyle \frac{\alpha \times \sigma }{2}}}{E}\right)}^2$

                              $={\left(\frac{1.96\times 3000}{1000}\right)}^2$

                             $\approx 35$

Thus,the sample size is$35$