In: Statistics and Probability
You manage a local tex-mex restaurant called “Garage Taco Bar.” You have recently switched all of your business to takeout due to the pandemic and you want to make sure you are still making enough money to stay open. The owner says that to keep everything running you need to be making more than $3,000 per day in takeout orders. Looking back on your records you take a random sample of 8 days and determine the following sample statistics. Assume the daily revenue is approximately normal.
Garage Taco Bar daily revenue: x1=$3,103, s1=$154
You decide you should run a hypothesis test to determine if you should stay open.
a. Define the hypotheses for this test. Is this a one-tailed or two-tailed test? If one-tailed, is it upper- or lower-tailed?
b. Give a rejection region for this test based on an α=0.05 significance level.
c. Solve for the test statistic and interpret the results of the test.