Question

In a study of the accuracy of fast food​ drive-through orders, Restaurant A had 211 accurate orders and 71 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: 0.226 < p < 0.323. What do you​ conclude? Need answer to both a. and b. Thanks.

Answer 1

The total no fo orders at restaurant A are 211+71=282 hence the proportion of orders that are not accurate are:

At a 95 % confidence level, the Z score is 1.96 computed using the Z table shown below.

The confidence interval is calculated as:

b) Now since the percentage of orders that are not accurate at Restaurant B: 0.226 < p < 0.323. so, if we compare both the percentage orders we get between 0.226 to 0.3025 there is a common percentage of orders that are incorrect. And in restaurant B the sample proportion will be

(0.226+0.323)/2=0.2745

And the margin of error will be 0.2745-0.226=0.0485