Question

Pascal Co. is considering replacing one of its software with a new software. Before a final decision is made, Pascal Co. has taken a sample of four hundred customers. After surveying the customers, 250 recommended that they would purchase the new software. Estimate the value of the population proportion. Develop a 99 percent confidence interval for the population proportion. Interpret your findings.

Answer 1

$\hat p=\frac{x}{n}=\frac{250}{400}=0.625.$

$99\%CI=(\hat p-z_{0.005}\sqrt{\frac{\hat p(1-\hat p)}{n}},\hat p+z_{0.005}\sqrt{\frac{\hat p(1-\hat p)}{n}})=$

$=(0.625-2.576\sqrt{\frac{0.625(1-0.625)}{400}},0.625-2.576\sqrt{\frac{0.625(1+0.625)}{400}})=$

$=(0.563,0.687).$

We are 99% confident that the population proportion of customers which are

recommended that they would purchase the new software lies between 0.563 and 0.687.