Chapter 8, Problem 8PT

To determine

To find: The number of observations.

Answer to Problem 8PT

The number of observations is 609.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Margin of error }\left(E\right)=2\\ \text{Standard}\text{deviation}\left(\sigma \right)=30\\ \text{Confidence level }=90\%\end{array}$

Formula used:

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

Calculation:

The value of $z_{\frac{\alpha }{2}}$ corresponding to $90\%$ confidence level is 1.645, which is obtained from the standard normal table.

The sample size can be calculated as:

  $\begin{array}{c}\text{Sample size}\left(n\right)={\left(\frac{z_{\frac{\alpha }{2}}\times \sigma }{E}\right)}^2\\ ={\left(\frac{1.645\times 30}{2}\right)}^2\\ =608.855\\ \approx 609\end{array}$

Thus, the number of observations is 609.

Hence, the correct option is (d).