Answer to Question #234804 in Statistics and Probability for Rishi Pakiry

Question

A random sample of 200 male shoppers in Pavilion shopping mall were interviewed to identify the reasons for coming to this particular mall. The factor of ' I prefer Knox brand in the mall ' was the most important reason for 120 of those interviewed. Estimate the likely percentage of all male shoppers who frequent this shopping mall primarily because of the Knox brand in the mall, using 97.5% confidence limits.

Answer 1

$CI=\hat P\pm Z_{\frac{\alpha}{2}}\sqrt{\frac{\hat{P}(1-\hat {P})}{n}}$

$\hat {p}=0.6$

$n=200$

$z_{0.0125}=12.2414$

97.5% CI is $0.6\pm2.2414(\sqrt{\frac{0.6\times0.4}{200}})$

$=0.6\pm00.07764$

$=[0.5224,0.67764]$