population proportion

**jax760** · February 3rd 2009, 10:04 PM

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?

**mr fantastic** · February 3rd 2009, 11:43 PM

Originally Posted by jax760

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?

$z_{\alpha/2} \sqrt{\frac{(0.4)(0.6)}{30}} = 0.10$ .

Solve the above equation for the critical value $z_{\alpha/2}$ and hence get the value of $\alpha$ . Use this value to get the required probability.

eg. If $z_{\alpha/2} = 1.96$ then (using tables) $\frac{\alpha}{2} = 0.025 \Rightarrow \alpha = 0.05$ and so the required probability would be 0.95.

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