Chapter 9.1, Problem 9.13E

To determine

To find the number of people they would need to interview.

Answer to Problem 9.13E

The number of people = 1844

Explanation of Solution

Given:

Confidence level = c = 0.99

Margin of error = 3% = 0.03

Formula:

  $n=p(1-p){\left(\frac{Zc}{E}\right)}^2$

Calculation:

Confidence level = c = 0.99, so level of significance = a = 1-0.99 − 0.01

Z critical value can be found either by using standard normal table or excel formula.

So, Z_c =Z_a/2 = Z_0.01/2

Using excel function, =ABS(NORMSINV(0.01/2))

Zc = 2.58

We don’t have preliminary population proportion, hence using p = 0.05

  $\begin{array}{l}n=0.5(1-0.5){\left(\frac{2.58}{0.03}\right)}^2\\ n\approx 1844\end{array}$