Question

In a study of the accuracy of fast food​ drive-through orders, Restaurant A had 217 accurate orders and 58 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: 0.195<p< 0.281. What do you​ conclude?

Answer 1

Solution:

Given: Restaurant A had 217 accurate orders and 58 that were not accurate.

n = 217 + 58 = 275

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

Formula:

where

and

We need to find zc value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Zc = 1.96

Thus

Thus

Part b. Compare the results from part​ (a) to this 95​% confidence interval for the percentage of orders that are not accurate at Restaurant​ B: 0.195<p< 0.281. What do you​ conclude?

Since lower limit of 95​% confidence interval for the percentage of orders that are not accurate at Restaurant​ B is within the limits of 95​% confidence interval for the percentage of orders that are not accurate at Restaurant A, we can say both confidence intervals for Restaurant A and Restaurant B overlap.

Thus we conclude that:
Since the two confidence intervals overlap, neither restaurant appears to have a significantly different percentage of orders that are not accurate.