Question

In a study of the accuracy of fast food​ drive-through orders, Restaurant A had

340340

accurate orders and

6060

that were not accurate.

a. Construct a

9595​%

confidence interval estimate of the percentage of orders that are not accurate.

b. Compare the results from part​ (a) to this

9595​%

confidence interval for the percentage of orders that are not accurate at Restaurant​ B:

0.1350.135less than<pless than<0.2010.201.

What do you​ conclude?

Answer 1

Total accurate orders = 340

Orders that are not accurate = 60

(a) 95% confidence interval = sample proportion +- margin of error

saple proportion of the percentage of orders that are not accurate = 60/400 = 0.15

standard error = sqrt [0.15 * (1-0.15)/400] = 0.01785

critical test statistic = 1.96

MOE = 1.96 * 0.01785 = 0.035

95% confidence interval = 0.15 +- 0.035 = (0.115, 0.185)

Here the given confidence interval coincides with the given confidence interval (0.135, 0.201)