Answer to Question #169492 in Statistics and Probability for Sunera

Question

Surveyors asked a random sample of women in a major city what factor was the most important in deciding where to shop. The results appear in the following table. If the sample size was 1200, estimate with 95% confidence the proportion of women who identified price and value as the most important factor.

Factor Percentage (%)

Price and Value 40

Quality and selection of merchandise 30

Service 15

Shopping environment 15

Answer 1

Solution:

Given, for price and value, $p=40\%=0.4, q=0.6$

$n=1200$

Standard error, $SE=\sqrt{\dfrac{pq}{n}}=\sqrt{\dfrac{0.4\times0.6}{1200}}=0.01414$

z-value for 95% confidence interval is 1.96.

So, required confidence interval $=1.96\pm SE=1.96\pm0.01414$

$=[1.94586, 1.97414]$