Many small restaurants in Portland, Oregon, and other cities across the United States do not take reservations. Owners say that with smaller capacity, no-shows are costly, and they would rather have their staff focused on customer service rather than maintaining a reservation system.† However, it is important to be able to give reasonable estimates of waiting time when customers arrive and put their name on the waiting list. The file RestaurantLine contains 10 observations of number of people in line ahead of a customer (independent variable x) and actual waiting time (in minutes) (dependent variable y). The estimated regression equation is:

ŷ = 4.35 + 8.81x

and MSE = 94.42.

(a)

Develop a point estimate (in min) for a customer who arrives with four people on the wait-list. (Round your answer to two decimal places.)

ŷ^* =  min

(b)

Develop a 95% confidence interval for the mean waiting time (in min) for a customer who arrives with four customers already in line. (Round your answers to two decimal places.)

min to  min

(c)

Develop a 95% prediction interval for Roger and Sherry Davy's waiting time (in min) if there are four customers in line when they arrive. (Round your answers to two decimal places.)

min to  min

(d)

Discuss the difference between part (b) and part (c).

The prediction interval is much  ---Select--- wider narrower than the confidence interval. This is because it is  ---Select--- more less difficult to predict the waiting time for an individual customer arriving with four people in line than it is to estimate the mean waiting time for a customer arriving with four people in line.

Harriet and Harry Combs (both 37 years old) are married and both want to contribute to a Roth IRA. In 2019, their AGI before any IRA contributions deductions is $50,000. Harriet earned $46,000 and Harry earned $4,000.

a. How much can Harriet contribute to her Roth IRA if they file a joint return?

b. How much can Harriet contribute if she files a separate return?

c. How much can Harry contribute to his Roth IRA if they file separately?

A study by a bank compared the mean savings of customers who were depositors for three years or less, with those who had been depositors for more than three years. The results of a sample are:

Depositors 3 years or less, sample size=100, mean saving balance=$1200, Population standard variation=$100

Depositors more than 3 years, sample size=150, mean saving balance=$1250, Population standard variation=$250

At the 0.10 significance level, can we conclude that those who had been depositing for more than three years carry higher balances than those who had been depositing three years or less? What is the p-value? Complete steps below.  

A. State the null hypothesis and the alternate hypothesis.

B. State the level of significance.

C. State the test statistic.

D. Formulate the decision rule.

E. Make a decision. Please show your work.

F. Determine the p-value (please show your work); Interpret the result of the hypothesis test.

A study by a bank compared the mean savings of customers who were depositors for three years or less, with those who had been depositors for more than three years. The results of a sample are:

Depositors 3 years or less, sample size=100, mean saving balance=$1200, Population standard variation=$100

Depositors more than 3 years, sample size=150, mean saving balance=$1250, Population standard variation=$250

At the 0.10 significance level, can we conclude that those who had been depositing for more than three years carry higher balances than those who had been depositing three years or less? What is the p-value? Complete steps below.  

A. State the null hypothesis and the alternate hypothesis.

B. State the level of significance.

C. State the test statistic.

D. Formulate the decision rule.

E. Make a decision. Please show your work.

F. Determine the p-value (please show your work); Interpret the result of the hypothesis test.

An Oxxo has a small parking lot with three spaces reserved for customers. If the store is open cars arrive and use a space with an average rate of 2 per hour. For n = 0, 1, 2, 3, the probability P n of that there are exactly n spaces occupied is P 0 = 0.1, P 1 = 0.2, P 2 = 0.4, P 3 = 0.3.
a) Describe the interpretation of this parking lot as a queuing system, that is, describe the parameters indicated. What level of service is provided?
b) Determine the basic performance measures: L and W of this queuing system.

Company MNO generates between 11000 and 15000 million dollars revenue per year. Suppose that the company's revenue stays within this range. Use an interest rate of 9.75% per year compounded continuously. Fill in the blanks in the paragraph below, rounding your answers to the nearest tenth.

The present value of MNO's revenue over a five year period is between _______________ and ______________ million dollars.

Over a twenty-five year period, the present value falls between ____________ and _____________ million dollars

section 10.4

Medical research has shown that repeated wrist extension beyond 20 degrees increases the risk of wrist and hand injuries. Each of 24 students at a university used a proposed new computer mouse design. While using the mouse, each student's wrist extension was recorded. Data consistent with summary values given in a paper are given. Use these data to test the hypothesis that the mean wrist extension for people using this new mouse design is greater than 20 degrees. (Use

? = 0.05.

Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

27 26 25 24 27 28 28 25 25 25 28 26

22 28 25 26 27 24 31 28 26 27 27 28

t =

P-value =

5. John the plumber has the following weekly demand for repairs by his business:

Q = 2,000 – 10(P)

Q = quantity of repairs demanded by customers per week.

P = average price per repair.

John chooses the price to charge to his customers (cause). The result (effect) will be the total number of repairs his customers want per week.

A.      Draw the demand curve faced by John the plumber. Numerically label its two end points.

B.      Create the table of numbers: P Q TR MR

P = average price per repair. You may skip numbers for price changes by $10 at a time.

TR = Total Revenue = PQ

MR = Marginal Revenue = (change in TR)/(change in Q)

Draw the MR curve on the diagram, as well/

C.      The MC (Marginal Cost) to John per repair is $20. What price (P) will be charged per repair, and how many repairs (Q) per week? Show it on your diagram with solved numbers.

D.      Label the Consumer Surplus on your diagram. Define Consumer Surplus, as well.

5. John the plumber has the following weekly demand for repairs by his business: Q = 2,000 – 10(P) Q = quantity of repairs demanded by customers per week. P = average price per repair. John chooses the price to charge to his customers (cause). The result (effect) will be the total number of repairs his customers want per week.

A. Draw the demand curve faced by John the plumber. Numerically label its two end points.

B. Create the table of numbers: P Q TR MR P = average price per repair. You may skip numbers for price changes by $10 at a time. TR = Total Revenue = PQ MR = Marginal Revenue = (change in TR)/(change in Q) Draw the MR curve on the diagram, as well/

C. The MC (Marginal Cost) to John per repair is $20. What price (P) will be charged per repair, and how many repairs (Q) per week? Show it on your diagram with solved numbers.

D. Label the Consumer Surplus on your diagram. Define Consumer Surplus, as well.