Question

In a study of the accuracy of fast food​ drive-through orders, Restaurant A had 240 accurate orders and 65 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: 0.195less thanpless than0.283. What do you​ conclude?

Construct a 95​% confidence interval. Express the percentages in decimal form.

Answer 1

a) The sample proportion of orders that are not accurate is computed here as:

= Number of inaccurate orders / Total orders

= 65 / (65 + 240)

= 0.2131

From standard normal tables, we have:
P( -1.96 < Z < 1.96) = 0.95

Therefore the confidence interval here is obtained as:

This is the required confidence interval here that is:

(16.71%, 25.91%)

b) As we are given the confidence interval for restaurant B here as:
( 19.5% , 28.3%)

Therefore as there is some overlapping between the 2 restaurants confidence interval, we cannot conclude anything about them.