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

Because you want a 99% confidence interval, your z-value is 2.576.

From a sample of 400 customers were found 250 customers would purchase the new software. So

$\hat{p} = \frac{250}{400} =0.625$

The formula for a confidence interval for a population proportion is

$\hat{p}±z \times \sqrt{\frac{\hat{p}(1- \hat{p})}{n}}$

Find

$\hat{p}\frac{1 - \hat{p}}{n} = 0.625 \frac{1-0.625}{400} = 0.0005859$

Take the square root to get 0.0242

Multiply your answer by z.

This step gives you the margin of error.

$2.576 \times 0.0242 = 0.0623$

Confidence interval:

0.625±0.0623

The interval = ((0.625-0.0623),(0.625+0.0623)) = (0.5627, 0.6873)

So, from 225 to 275 customers would purchase the new software.