The mean diastolic blood pressure for a random sample of 70 people was 90 millimeters of mercury. If the standard deviation of individual blood pressure readings is known to be 11 millimeters of mercury, find a 90% confidence interval for the true mean diastolic blood pressure of all people. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. What is the lower limit of the 90% confidence interval? What is the upper limit of the 90% confidence interval?

1) what does it mean if a psychological scientist runs an experiment and finds a statistically significant result? a) The likelihood of a Type I error is greater than 5% b) The likelihood that the result was due to chance is low enough to reject the null hypothesis c) The theory that the scientist was testing is proven

2) What decision must a psychological scientist make if an obtained p-value is greater than the adopted alpha? a) To accept the null hypothesis b) To reject the null hypothesis c) That there is a type I error

3) What does a psychological scientist conclude if an obtained p-value is less than the adopted alpha? a) The likelihood that the result was due to chance is too high to reject the null hypothesis b) The effect of the IV manipulation is statistically significant c) The likelihood of a type II error is greater than 5%

4) With all else being equal, what happens to the inferential stat. we calculate to determine whether 2 groups differ, as the difference between their means increases? a) the Pearson's r increases b) The t-score increase c) The variance decreases d) The sum of squares decrease

5) All else being equal, what happens to the inferential stat. we calculate to determine whether 2 groups differ, as the variance of each of the groups increases? a) The Pearson's r decreases b) The t-score decreases c) The mean increases d)The sum of squares increases

6) All else being equal, what happens to the p-value that corresponds with our inferential stat., as the difference between the means of two groups increases? a) it does not change b) It increases c) It decreases d) it approaches 1.0

It has determined that a funded reserve is its preferred method of retention and it would like to make sure that it has enough to cover losses in 97.5% (2.5% on each side of the distribution) of all situations with losses normally distributed. How much does the retailer need to have in its funded reserve if the expected losses are $2.5m and standard deviation is $500k?

A) An Olympic archer is able to hit the bull’s eye 80% of the time. Assume each shot is independent of the others. She will shoot 6 arrows. Let X denote the number of bull’s eyes she makes.

Find the mean of the probability distribution of X. Do not round

B) The GPA of students at a college has a mean of 2.9 and a standard deviation of 0.3. Scores are approximately normally distributed.

Suppose that the top 6% of students are eligible for the Honors Program. Find the GPA which is the cutoff score for students to qualify for this program. Round to the nearest hundredth.

Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, x has an approximately normal distribution with mean μ = 4.2 and standard deviation σ = 0.5. (a) Convert the x interval, 4.5 < x, to a z interval. (Round your answer to two decimal places.) < z (b) Convert the x interval, x < 4.2, to a z interval. (Round your answer to two decimal places.) z < (c) Convert the x interval, 4.0 < x < 5.5, to a z interval. (Round your answers to two decimal places.) < z < (d) Convert the z interval, z < −1.44, to an x interval. (Round your answer to one decimal place.) x < (e) Convert the z interval, 1.28 < z, to an x interval. (Round your answer to one decimal place.) < x (f) Convert the z interval, −2.25 < z < −1.00, to an x interval. (Round your answers to one decimal place.) < x < (g) If a female had an RBC count of 5.9 or higher, would that be considered unusually high? Explain using z values. Yes. A z score of 3.40 implies that this RBC is unusually high. No. A z score of −3.40 implies that this RBC is unusually low. No. A z score of 3.40 implies that this RBC is normal.

3. [13 marks] A company is interested in forecasting demand for a product. They have reason to believe that the demand is not affected by any seasonal changes and that it does not increase or decrease systematically over time. They have data for the last 9 periods (below).

In each part of this question, show your work: show the equation you use, how you plug in, and your final answer. Please do not round any answers. Hint: see lecture 22 example 3.

a) [3 marks] Use a 4-period moving average to forecast demand for period 10.

b) [3 marks] Use a 3-period weighted moving average to forecast demand for period 10 using weights of 0.6, 0.3, and 0.1, respectively. Show your work.

c) [3 marks] Suppose the forecast for period 9 was 235 units. Use exponential smoothing with a smoothing constant of 0.6 to forecast demand for period 10.

d) [4 marks] Suppose the actual demand in period 10 was 211 units. Which of your forecasting methods from parts a through c performed best, and why? Please provide a table similar to the one shown on slide 48 of lecture 22, and make your conclusion based on your table.

1. Shown below is a partial Excel output from a regression analysis.

A pharmaceutical company is developing a treatment for blindness caused by diabetic retinopathy. Thus, 5 patients with advanced retinopathy were selected. For each patient, their left eye was treated and their right eye was left untreated. The time to blindness (in months) was recorded for both eyes and all patients as follows:

Calculate a 95% confidence interval to assess the difference in time to blindness due to treatment.

Find the indicated confidence interval. Assume the standard error comes from a bootstrap distribution that is approximately normally distributed.

A 90% confidence interval for a mean μ if the sample has n=100 with x¯=22.1 and s=5.6, and the standard error is SE=0.56.

Round your answers to three decimal places.

The 90% confidence interval is Enter your answer; The 90% confidence interval, value 1 to Enter your answer; The 90% confidence interval, value 2 .

Regional Airlines is establishing a new telephone system for handling flight reservations. During the 10:00 AM to 2:00 PM time period, calls to the reservation agent occur randomly at an average rate of one call every 3.75 minutes. Historical service time data show that a reservation agent spends an average of 3 minutes with each customer. The waiting line model assumptions of Poisson arrivals and exponential service times appear reasonable for the telephone reservation system.
At a planning meeting, Regional’s management team agreed that an acceptable customer service goal is to answer at least 75% of the incoming calls immediately. During the planning meeting, Regional’s vice president of administration pointed out that the data show that the average service rate for an agent is faster than the average arrival rate of the telephone calls. The vice president’s conclusion was that personnel costs could be minimized by using one agent and that single agent must be able to handle the telephone reservations and still have some idle time. The vice president of marketing restated the importance of customer service and expressed support for at least two reservation agents.
We already analyzed the single-agent system’s performance according to the opinion of vice president of administration. We concluded that operating the telephone reservation service with only one ticket agent appears unacceptable because they won’t be able to meet their goal. Answer to the following questions to evaluate the opinion of vice president of marketing:

1. What is the service rate for the 2-agent system? Interpret the number.





2. What percentage of time both agents are idle?





3. What percentage of time a caller will be blocked if the system design does not allow callers to wait?



4. What percentage of time only one ticket agent is busy?

What is a Type I Error? What is the impact on Type II Error if we reduce the likelihood of Type I Error? Please upload in Microsoft Word.

The experiment data in below table was to evaluate the effects of three variables on invoice errors for a company. Invoice errors had been a major contributor to lengthening the time that customers took to pay their invoices and increasing the accounts receivables for a major chemical company. It was conjectured that the errors might be due to the size of the customer (larger customers have more complex orders), the customer location (foreign orders are more complicated), and the type of product. A subset of the data is summarized in the following Table.

Table: Invoice Experiment Error

Customer Size: Small (-), Large (+)

Customer Location: Foreign (-), Domestic (+)

Product Type: Commodity (-), Specialty (=)

Reference: Moen, Nolan, and Provost (R. D. Moen, T. W. Nolan and L. P. Provost. Improving Quality through Planned Experimentation. New York: McGraw-Hill, 1991)

Use the date in table above and answer the following questions in the space provided below:

1. What is the nature of the effects of the factors studied in this experiment?
2. What strategy would you use to reduce invoice errors, given the results of this experiment?

Problem 1   (TAY 44-45/161 adjusted)                           The Metro Food Services Company delivers fresh sandwiches each morning to vending machines throughout the city. The company makes three kinds of sandwiches – ham and cheese, bologna, and chicken salad. A ham and cheese sandwich requires a worker 0.90 minutes to assemble, a bologna sandwich requires a worker 0.80 minutes, and a chicken salad sandwich requires a worker 1.00 minutes to make. The company has 6 workers available each night to assemble sandwiches (i.e. 2,880 minutes). Vending machine capacity is available for 3,000 sandwiches each day. The profit for a ham and cheese sandwich is 70¢ (i.e. $0.70), the profit for a bologna sandwich is 85¢, and the profit for a chicken salad sandwich is 75¢. The company knows from past sales records that their customers buy as many or more of the ham and cheese sandwiches than the other two sandwiches combined. But customers need a variety of sandwiches available, so Metro stocks at least 300 of each sandwich type. Metro management wants to know how many of each sandwich it should stock to maximize profit.

Formulate this decision question as a Linear Programming Model. Define the variables, write down the constraints and the objective function in mathematical (algebraic) terms (variables, inequalities, etc.).

Find the optimal solution using SOLVER.

Answer as many parts below as possible without re-running Solver. (do each part independently from the others) Use the SENSITIVITY REPORT whenever possible.

If Metro Food Services could hire another worker and increase its available assembly time by 480 minutes, or increase its vending machine capacity by 200 sandwiches, which should it do? How much additional profit would your decision result in?

What would the effect be on the optimal solution if the profit for a ham and cheese sandwich were increased to 80¢?   to 90¢?  

Roulette wheels have 38 numbers (1 through 36 plus 0 and 00) of which 18 are red, 18 are black, and the 0 and 00 are green. A bettor may place a $1 bet on any one of the 38 numbers. The bettor wins $35 (bettor gets his $1 back) if the ball lands on his number, otherwise he loses his bet.

a) Find the expected value of the game.

b) What is wrong about how the casino pays a winner if they bet on a single number?