Question

In a study of fast food accuracy on drive-thru orders, Burger King had 264 accurate orders and 54 that were not accurate.

a. Construct a 95% CI for the percentage of orders that are not accurate.

b. A similar survey at McDonald's yield a 95% CI of inaccurate orders of 6.2%<P<15.9%. Comparing the two results, what do you find?

Answer 1

Solution:

Given: In a study of fast food accuracy on drive-thru orders, Burger King had 264 accurate orders and 54 that were not accurate.

n= 264 + 54 = 318

Part a. Construct a 95% CI for the percentage of orders that are not accurate.

where

and

We need to find z_c 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 : Z_c = 1.96

thus

Thus

Part b. A similar survey at McDonald's yield a 95% CI of inaccurate orders of 6.2%<P<15.9%. Comparing the two results, what do you find?

Upper limit 15.9% is within the limits of confidence interval obtained in part a) , thus both confidence interval overlaps.

thus correct answer is:

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