Chapter 13.7, Problem 9PPS

To determine

The sampling method used by the school committee is valid or not and the number of students will participate in the school program is to be estimated.

Answer to Problem 9PPS

Yes. The sampling method is valid. $144$ students will participate in the school program out of $576$ students.

Explanation of Solution

Given:

  $\begin{array}{l}p=25\%\\ N=576\end{array}$

Concept Used:

The method to choose sample or each member of the subset which has the equal value of probability of being chosen in a statistical population subset is known as a simple random sample.

Calculation:

The sampling of students is valid. In this problem there is use of simple random sample which is a type of the unbiased sample because school committee selected $25\%$ students at a mall on a Saturday afternoon.

Numbers of students will participate in the school program of $576$ students are calculated as:

  $\begin{array}{l}E=p\times N\\ E=25\%\times 576\\ E=0.25\times 576\\ E=144\end{array}$

Conclusion:

Hence, number of students will participate in the school program of $576$ students are $E=144$ .