1.

You manage a local tex-mex restaurant called “Garage Taco Bar.”You have recently switched all of your business to takeout due tothe pandemic and you want to make sure you are still making enoughmoney to stay open. The owner says that to keep everything runningyou 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 anddetermine the following sample statistics. Assume the daily revenueis approximately normal.

Garage Taco Bar daily revenue:x1=$3,103,s1=$154

You decide you should run a hypothesis test to determine if youshould stay open.

a. Define the hypotheses for this test. Is this a one-tailed ortwo-tailed test? If one-tailed, is it upper- or lower-tailed?

b. Give a rejection region for this test based on anα=0.05 significance level.

c. Solve for the test statistic and interpret the results of thetest.

2. One of your workers has a friend at a competing restaurant“Dos Rios,” and they tell you that they have also thought aboutclosing. You find that Dos Rios has also randomly sampled days toestimate their daily revenue. Your worker’s friend gives you thefollowing statistics based on 10 randomly sampled days. Assume thedistribution is approximately normally distributed, and that thetrue variance is equal to that of “Garage”.

Dos Rios daily revenue: x2= $2,791 S2= $151

You go to the owner with this information, and they tell youthat knowing this, “Garage Taco Bar” should stay open if they aremaking significantly more money per day than Dos Rios.

You decide you need to run a new hypothesis test.

a. Define the parameter of interest in this test, and calculatethe point estimate.

b. Find a rejection region for this test based anα=0.05 significance level and calculate the teststatistic.

c. Interpret the results of the test.