Question

In a study of the accuracy of fast food drive-through orders, McDonald's had 35 orders that were not accurate among 367 orders observed. Construct a 95% confidence interval for the proportion of orders that are not accurate.

(a) Identify the best point estimate of the population proportion p (all McDonald's order that are not accurate).

(b) Identify the value of the margin of error E?

(c) Find the confidence interval for the proportion of McDonald's orders that are not accurate.

(d) Write a statement that correctly interprets the confidence interval.

Answer 1

(a) The best point estimate of the population proportion, p = 35/367 = 0.0954

(b) Corresponding to 95% confidence interval, the z score = 1.96

The value of the margin of error, E =

=

= 0.03

(c) The confidence interval for the proportion of McDonald's orders that are not accurate = (p - E, p + E)

= (0.0654, 0.1254)

(d) We are 95% confident that the mean population proportion of McDonald's orders that are not accurate falls in the range 0.0654 and 0.1254