The Coca-cola Company has 40% of the cola market. The probability that a sample proportion for n=30 falls within 0.10 of the true population proportion of .40, which represents the proportion of cola drinkers who prefer a coca-cola drink is?
The Coca-cola Company has 40% of the cola market. The probability that a sample proportion for n=30 falls within 0.10 of the true population proportion of .40, which represents the proportion of cola drinkers who prefer a coca-cola drink is?
$\displaystyle z_{\alpha/2} \sqrt{\frac{(0.4)(0.6)}{30}} = 0.10$.
Solve the above equation for the critical value $\displaystyle z_{\alpha/2}$ and hence get the value of $\displaystyle \alpha$. Use this value to get the required probability.
eg. If $\displaystyle z_{\alpha/2} = 1.96$ then (using tables) $\displaystyle \frac{\alpha}{2} = 0.025 \Rightarrow \alpha = 0.05$ and so the required probability would be 0.95.