Question

Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of a new toothpaste package. She plans to use a 95% confidence interval estimate of the proportion of households which prefer the new packages; she will accept a 0.05 error. Previous studies indicate that new packaging has an approximately 70% acceptance rate. The sample size should be at least _______.

Answer 1

Answer: 323

Step-by-step explanation:

The formula to calculate the sample size for proportion is given by :_

$n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2$

Given : Significance level : $\alpha: 1-0.95=0.095$

Critical value : $z_{\alpha/2}=1.96$

Margin of error : $E=0.05$

The proportion of successes : $p=0.70$

Now, the required sample size will be :-

$n=0.70(0.30)(\dfrac{(1.96)}{0.05})^2=322.6944\approx323$

Hence, the minimum required sample size = 323