Question

In a study of the accuracy of fast food​ drive-through orders, Restaurant A had 206 accurate orders and 57 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: 0.198less thanpless than0.299. What do you​ conclude?

Answer 1

sample proportion, = 0.2167
sample size, n = 263
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.2167 * (1 - 0.2167)/263) = 0.0254

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.2167 - 1.96 * 0.0254 , 0.2167 + 1.96 * 0.0254)
CI = (0.167 , 0.266)

b)
The calculated CI for restaurant A overlaps with the CI for restaurant B.
This means that there is not significant difference in the proportion of not accurrate orders between two restaurants.