Question

Suppose a shoe store wants to determine the current percentage of customers who are males. How many customers should the company survey in order to be 90% confident that the estimated (sample) proportion is within 3 percentage points of the true population proportion of customers who are males?

Answer 1

Answer: 1067

Step-by-step explanation:

Given : Level of confidence = 0.90

Significance level : $\alpha=1-0.90=0.1$

By using the normal distribution table,

Critical value : $z_{\alpha/2}=1.96$

Margin of error : $E=3\%=0.03$

The formula to find the population proportion if prior proportion of population is unknown  :-

$n=0.25(\dfrac{z_{\alpha/2}}{E})^2$

$\Rightarrow n=0.25(\dfrac{1.96}{0.03})^2=1067.111111\approx1067$

Hence, the company should survey minimum sample having size  =1067