Question

1.

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.

2. One of your workers has a friend at a competing restaurant “Dos Rios,” and they tell you that they have also thought about closing. You find that Dos Rios has also randomly sampled days to estimate their daily revenue. Your worker’s friend gives you the following statistics based on 10 randomly sampled days. Assume the distribution is approximately normally distributed, and that the true 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 you that knowing this, “Garage Taco Bar” should stay open if they are making 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 calculate the point estimate.

b. Find a rejection region for this test based an α=0.05 significance level and calculate the test statistic.

c. Interpret the results of the test.

Answer 1