Question

In a study of the accuracy of fast food drive-through orders, Restaurant A had 313 accurate orders and 70 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: 0.167 < p < 0.235. 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. No conclusion can be made because not enough information is given about the confidence interval for Restaurant B.

B. 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.

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

D. 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.

Answer 1

The statistical software output for this problem is:

Hence,

a) 90% confidence interval:

0.185 < p < 0.262

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