In this problem, you will develop a hypothesis test for a new situation. Suppose that you believe the waiting time until you are served at the drive-thru window at the Big Burger Barn is a random variable with an exponential distribution but with unknown λ. The sign at the drive-thru window says that the average wait time (after placing the order until it is ready at the window) is 1 minute. You actually wait 2 minutes and 12 seconds. A friend in the car with you says that this is outrageous since it is more than twice as long as the average is supposed to be. He is sure that the claimed average must be incorrect.
a) What are the null and alternative hypotheses?
b) What is your test statistic and what distribution does it have if the null hypothesis is true?
c) Determine the p-value for your particular sample. d) Write a sentence that explains clearly to your friend the meaning of that pvalue. Your friend has not yet been fortunate enough to take a statistics course, so don't use statistical jargon.
e) What is the shortest wait time that would cause you to be suspicious of Big Burger Barn's claim? Explain.
f) How would things change if you decided to return 5 times and record the wait time each time? Do we have appropriate methods to deal with this situation?