Question

A newspaper wants to estimate the approval rating for the current president by using the confidence interval method. The ideal confidence interval should have a margin of error (E) of 0.02 with 90% confidence level. The newspaper needs to conduct a survey to achieve this. Find the minimum sample size for this survey. 300 4145 1024 2401 1692

Answer 1

The values provided in the above question asr as belows

Margin of error = E = 0.02

Confidence level = 90% = 0.90

The significant level of $\alpha$ = 1 - 0.90 = 0.10

We have to find the Zc using following command in Excel

For symmetric distribution we use significant level $\alpha$ /2 for finding critical value

critical value = Z$\alpha$/2 = Z0.05 = -1.645

We write $\left | z_{0.05} \right | = 1.645$

The formula is used for the finding the minimum sample size for this survey is as

Sample size =  $n = \frac{1}{4}*(\frac{Z_{\alpha /2}}{E})^2$

$n = \frac{1}{4}*(\frac{1.645}{0.02})^2$

n = 1691.266 $\approx 1692$ (Sample size is always express in interger so we round up it in interger value)

The minimum sample size for this survey is 1692