Chapter 8, Problem T8.8SPT

To determine

To find: The number of observations.

Answer to Problem T8.8SPT

The number of observations is 25.

Explanation of Solution

Given:

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

Formula used:

The formula to compute the sample size is:

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

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 number of observations can be calculated as:

  $\begin{array}{c}n={\left(\frac{z_{\frac{\alpha }{2}}\times \sigma }{E}\right)}^2\\ ={\left(\frac{1.645\times 30}{2}\right)}^2\\ =24.675\\ \approx 25\end{array}$

Hence, the sample size is 25.

Thus, the correct option is (a).