Question

In a study of the accuracy of fast food​ drive-through orders, Restaurant A had 257 accurate orders and 58 that were not accurate.a. Construct a 90​% confidence interval estimate of the percentage of orders that are not accurate.

b. Compare the results from part​ (a) to this 90​% confidence interval for the percentage of orders that are not accurate at Restaurant​ B: 0.164 < p < 0.234 What do you​ conclude?

a. Construct a 90​% confidence interval. Express the percentages in decimal form.

< p <

​(Round to three decimal places as​ needed.)

b. Choose the correct answer below.

A. Since the two confidence intervals​ overlap, neither restaurant appears to have a significantly different percentage of orders that are not accurate.

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.

C. Since the upper confidence limit of the interval for Restaurant B is higher than both the lower and upper confidence limits of the interval for Restaurant​ A, this indicates that Restaurant B has a significantly higher percentage of orders that are not accurate.

D. No conclusion can be made because not enough information is given about the confidence interval for Restaurant B.

Answer 1

The statistical software output for this problem is:

Hence,

a) 90% confidence interval:

0.148 < p < 0.220

b) Since the two confidence intervals​ overlap, neither restaurant appears to have a significantly different percentage of orders that are not accurate. Option A is correct.