Question

1.3 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. (10)

Answer 1

Solution:

Given: sample Size =n=200

no. of success =x=120

Point estimate $(\bar{p})=\dfrac{x}{n}=0.600$

Confidence Level (CL)=0.975

$\alpha=1-\mathrm{CL}=0.025$

$\begin{aligned} Z_{\text {critical }}=Z_{\alpha / 2}=& 2.24 \quad \text { [Using tables}] \end{aligned} \\\text { Standard Error(SE })=\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}=0.035 \\ \text { margin of error(E) }=Z_{\alpha / 2}(\mathrm{SE}) =0.078 \\ \text { Lower Limit }=\bar{p}-\mathrm{E}=0.5224 \\ \text { Upper Limit }=\bar{p}+\mathrm{E}=0.6776 \\ \text{Thus, 97.5 \% confidence interval estimate is (0.5224,0.6776)}$