Answer to Question #237565 in Statistics and Probability for suvi

Question

A random sample of 200 male shoppers in Pavilion shopping mall were interviewed to identify their 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

SOLUTION

The best point estimate available, $\hat{p} = \frac{120}{200}=0.6$

Given the confidence level, CI = 0.975

$\alpha=1-CI=1-0.975=0.025$

Z_critical $=Z_{\frac{\alpha}{2}}=0.025$ from using the table

SE $=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.035$

The margin error, E $=Z_{\frac{\alpha}{2}}*(SE)=0.078$

Lower limit $=(\overline{p}-E)=0.5224$

Upper limit $=(\overline{p}+E)=0.6776$

The lower percentage $=97.5-0.5224=96.9776\%$

The upper percentage $=97.5+0.6776=98.1776\%$

ANSWER: The likely percentage of all male shoppers visiting the shop will range from $96.9776\%$ to $98.1776\%$