Question

In a study of the accuracy of fast food​ drive-through orders, Restaurant A had 221 accurate orders and 64 that were not accurate.

a. Construct a 95​% confidence interval estimate of the percentage of orders that are not accurate.

b. Compare the results from part​ (a) to this 95​% confidence interval for the percentage of orders that are not accurate at Restaurant​ B: 0.196<p<0.304.

What do you​ conclude?

Answer 1

a)

n= 221 + 64= 285

x= 64

Formula for confidence interval is

Where Zc is the z critical value for c= 95%

We get,

Zc=1.96

0.17611 < P < 0.27301

We get confidence interval as

0.176 < p < 0.273

b)

The lower confidence limit of the interval for Restaurant B is higher than the lower confidence limit of the interval for Restaurant A and the upper confidence limit of the interval for Restaurant B is also higher than the upper confidence limit of the interval for Restaurant A. Therefore, Restaurant B has a significantly higher percentage of orders that are not accurate.