Question

3.Jethro’s BBQ Food Truck.Jethro’s BBQ is a local chain of restaurants located at centralIowa. Bruce, the owner of the restaurant located at Ames, is thinking about expanding his business using a food truck that would be located during weekdays at the ISU campus. One important aspect for the planning of such project is to determine what would be a reasonable price range for the food. The prices need to be appealing and affordable for college students and at the same time be high enough so the food truck ends up being profitable. The first goal Bruce sets is to determine how much money on average ISU students spend buying lunch during weekdays. Bruce spent a morning asking students all around campus how much money they spend on buying lunch during weekdays. He got an answer from 87 students yielding to an average daily spend of $9.27. Bruce found out that five years ago ISU conducted a very complete study on students spending, and the standard deviation back then for daily spend on lunch was $1.78. Bruce assumed the standard deviation has not changed.(

a)In the context of this problem, what does μ represent?

(b) In the context of this problem, would z critical values or t critical values be more appro-priate?i. z critical values would suffice in this case since our standard deviation is ”known.” ii. t critical values would suffice in this case since our standard deviation is unknown. iii.z critical values would be more appropriate since our sample size is large enough.iv. t critical values would be more appropriate since our sample size is not large enough.

(c) Calculate the lower bound for a 95% confidence interval, for the unknown population mean,μ, by answering the following questions below. Round to two decimal places .i. Find the appropriate critical value. (Give your answer to 2 decimal places.)ii. What is the value of the lower bound of the 95% confidence interval? (Round your answer to 2 decimal places).

(d) Similarly, now calculate a 85% confidence interval for the unknown population mean,μ.i. Find the positive z-score (z∗) for the corresponding confidence level. (Round your answer to 2 decimal places). ii. Find the lower and the upper bound of the confidence interval. (Round your answer to 2 decimal places).

iii.[Select All That Apply.]Which of the following represents a correct interpretation of the 85% confidence interval forμin the context of the problem?

A. If we take 100 samples and calculate 85% confidence intervals for each, we expect85 out of the 100 intervals to contain the average amount of money ISU students spend buying lunch during weekdays.

B. We are 85% confident that the sample mean of how much the 87 ISU students sampled spend buying lunch during weekdays ($9.27) falls between $8.90 and $9.64.

C. There is a 85% chance the sample mean of how much the 87 ISU students sampled spend buying lunch during weekdays ($9.27) falls between $8.90 and $9.64.2

D. We are 85% confident that the average amount of money ISU students spend buying lunch during weekdays falls between $8.90 and $9.64.

iv.Suppose that the amount of money spend buying lunch during weekdays by all ISU students does not follow a Normal distribution. Is the confidence interval trust worthy? That is, do you think you can really be 85% confident? Explain

Answer 1