In a recent study of drive-through orders at Burger King, they found out that 365 were accurate and 71 were not accurate.
a) Construct a 95% confidence interval for the population percentage of their drive-through order that were not accurate.
b) If Burger King claims to have an accuracy of 85% on all drive-through orders, test the claim at the 0.05 levels of significance.
Compute for the value of the point estimate. There are successes (orders that were not accurate) out of drive-through orders in the study, so
Because we want a 95% confidence interval, we have , so
So, we have everything we need to solve for the lower and upper bounds of the confidence interval.
The lower bound is:
The upper bound is:
Therefore, we are 95% confident that the percentage of Burger King’s drive-through orders that were not accurate is between 12.8% and 19.8%.
The null and alternative hypothese are:
The sample proportion is
The test statistic is
Because this is a two-tailed test, we determine the critical value at level of significance to be . The critical region is shown in the figure below.
Since the test statistic is not in the rejection region, we FAIL TO REJECT the null hypothesis.
There is sufficient evidence at the level of significance to conclude that Burger King’s accuracy in their drive-through orders is 85%.