Question

McDonalds waiting time from order to pick-up has gotten a lot of attention in the media recently. Following is the distribution of waiting time from order to pick-up for McDonalds. According to the 2013 Drive-Thru Performance Study by QSR magazine, customers are waiting longer than ever to drive away with a quick meal, even at fast food behemoths like McDonald’s. One of the McDonalds branches reported that its average wait time climb to 188.5 seconds from order to pick-up. This has become a big concern for the top managers at McDonalds. To assess the validity of this claim and see whether the average time in general has increased, two research groups are asked to do the hypothesis testing and share their results.

Group 1 studied on 50 branches of McDonalds. The average waiting for these 50 branches is 185 seconds with the standard deviation of 25.

Group 2 studied on 25 branches of McDonalds. The average waiting time for these 25 branches is 190 seconds with standard deviation of 30 seconds. Median:175, Mean:180

a) Write the appropriate null and alternative hypotheses.

b) Appropriately choose one of the groups and explain why you choose that group.

c) Use the information from that group and at 0.06 level of significance test your hypothesis. (test-statistic approach) d) Do the test using the p-value.

e) Show all your answers on a normal distribution graph.

f) Share your results with your managers.

g) Use the information from your chosen group and construct a 92% confidence interval to estimate the average waiting from order to pick up for McDonalds. Also, find the margin of error.

h) Express your result in part g in a common language.

Answer 1

For Group 1 , sample size is greater than 30, we can approximate z test.

For Group 2 , sample size is smaller  than 30, we can use t- test.

a) We will use group 1 because as sample size is greater than group 2. So, it will have more precise results. As well as the standard deviation is also small in group 1.

b) The null and alternative hypothesis is

f) We fail to reject the null hypothesis. This means the branch report is correct that is branches reported that its average wait time climb to 188.5 seconds from order to pick-up.

g)

The margin of error is computed as

h) From (g) we have that the 92% confidence interval contains 188.5. So, we can say that with 92% Confidence there is chance that waiting has climbed to 188.5