Suppose you are playing a game with a friend in which you bet ? dollars on the flip of a fair coin: if the coin lands tails you lose your ? dollar bet, but if it lands heads, you get 2? dollars back (i.e., you get your ? dollars back plus you win ? dollars).

Let ? = "the amount you gain or lose."

(a) What is the expected return ?(?) on this game? (Give your answer in terms of ?)

Now, after losing a bunch of times, suppose you decide to improve your chances with the following strategy: you will start by betting $1, and if you lose, you will double your bet the next time, and you will keep playing until you win (the coin has to land heads sometime!).

Let ? = "the amount you gain or lose with this strategy".

(b) What is the expected return ?(?) with this strategy? (Hint: think about what happens for each of the cases of ?=1,2,3… flips).

(c) Hm ... do you see any problem with this strategy? How much money would you have to start with to guarantee that you always win?

(d) Suppose when you apply this strategy, you start with $20 and you quit the game when you run out of money. Now what is ?(?)?

An F-statistic is:

The characteristics of the F-Distribution include all but:

Which statement about the F-distribution is correct:

Analysis of Variance is used to:

In what follows use any of the following tests/procedures: Regression, multiple regressions, confidence intervals, one-sided t-test or two-sided t-test. All the procedures should be done with 5% P-value or 95% confidence interval Upload CARS data. SETUP: It is believed that Mercedes’ prices (Suggested price) are different than BMW’s. Given the data your job is to confirm or disprove this belief. (CAREFULL: sort the data in order to extract the needed information). 1. What test/procedure did you perform? a. One-sided t-test b. Two-sided t-test c. Regression d. ??Confidence interval 2. What is the P-value/margin of error? a. 0.161902527 b. 0.080951264 c. 6.149555 d. 8.065421 e. ??None of these 3. Statistical interpretation a. Since P-value is very small we are confident that the average Price is above 40000. b. Since P-value is large we cannot claim that the averages are different. c. Since P-value is very small we are confident that the slope of regression line is not zero. d. ??None of these. 4. Conclusion a. Yes, I am confident that the above assertion is correct. b. No, we cannot claim that the above assertion is correct. DATA: MERCEDES BMW 26060 30795 28370 37995 32280 30245 33480 35495 35920 36995 37630 37245 52120 39995 94820 44295 128420 44995 45707 54995 52800 69195 48170 73195 57270 74320 86970

Bay Oil produces two types of fuels (regular and super) by mixing three ingredients. The major distinguishing feature of the two products is the octane level required. Regular fuel must have a minimum octane level of 90 while super must have a level of at least 100. The cost per barrel, octane levels and available amounts (in barrels) for the upcoming two-week period appear in the table below. Likewise, the maximum demand for each end product and the revenue generated per barrel are shown below.

Develop and solve a linear programming model to maximize contribution to profit.

If required, round your answers to one decimal place. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) If the constant is "1" it must be entered in the box.

R1, R2, R3, S1, S2, S3 ≥ 0

What is the optimal contribution to profit?

Maximum Profit = $  by making   barrels of Regular and   barrels of Super.

Give an example of how the niche-picking genotype-environment correlation could be manifest.   

The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk-free securities to stabilize income. The various revenue-producing investments together with annual rates of return are as follows:

The credit union will have $2 million available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments:

• Risk-free securities may not exceed 30% of the total funds available for investment.

• Signature loans may not exceed 10% of the funds invested in all loans (automobile, furniture, other secured, and signature loans).

• Furniture loans plus other secured loans may not exceed the automobile loans.

• Other secured loans plus signature loans may not exceed the funds invested in risk-free securities.

How should the $2 million be allocated to each of the loan/investment alternatives to maximize total annual return?

What is the projected total annual return?

Annual Return = $

For each of the topics, choose an 'application' for using the model to solve a business problem. (In what area could you see applying some of the strategies presented in the chapter, and audio. Provide a short example and set up the problem solution.

1) Queuing: a) Where would you apply some of this knowledge? b) Provide a quick setup with all the variables of the application you chose

2) Inventory Management:  a) Where would you apply some of this knowledge? b) Provide a quick setup with all the variables of the application you chose

3) Linear Programming:  a) Where would you apply some of this knowledge? b) Provide a quick setup with all the variables of the application you chose

Please attach excel file

an energy drink manufacturer has developed four new drink flavors and would like to conduct a taste test to collect data on customers' preferences. Six people were asked to sample and rate each flavor on a scale of 1−20. Complete parts a through c below.

Click the icon to view the flavor ratings.

what conclusions can be made about the preference for the four flavors?
a. Using α=0.05 ,Click the icon to view an excerpt from a table of critical values of the studentized range.

What are the correct null and alternative hypotheses?

A.

H 0 : μ1=μ2=μ3=μ4

H 1 : Not all the μ’s are equal

B.

H 0: Not all the μ 's are equal

H 1 : μ1=μ2=μ3=μ4

C.

H 0 : μ1=μ2=μ3=μ4

H 1 : μ1≠μ2≠μ3≠μ4

D.

H 0 : μ1≠μ2≠μ3≠μ4

H 1: μ1=μ2=μ3=μ4

What is the test statistic?

Fx=

(Round to two decimal places as needed.)

What is the p-value?

The p-value is .

(Round to three decimal places as needed.)

What is the correct conclusion?

A.

Reject H 0. There is insufficient evidence that any of the drinks were preferred differently.

B.

Do not reject H 0. There is insufficient evidence that any of the drinks were preferred differently.

C.

Reject H 0. There is evidence that some of the drinks were preferred differently.

D.

Do not reject H 0. There is evidence that some of the drinks were preferred differently.

b. Was blocking effective? Why or why not?

What are the correct null and alternative hypotheses?

A.

H 0 : Not all the μBL 's are equal

H 1 : μBL1=μBL2=μBL3=μBL4=μBL5=μBL6

B.

H 0 : μBL1≠μBL2≠μBL3≠μBL4≠μBL5≠μBL6

H 1 : μBL1=μBL2=μBL3=μBL4=μBL5=μBL6

C.

H 0: μBL1=μBL2=μBL3=μBL4=μBL5=μBL6

H 1 : μBL1≠μBL2≠μBL3≠μBL4≠μBL5≠μBL6

D.

H 0: μBL1=μBL2=μBL3=μBL4=μBL5=μBL6

H 1: Not all the μBL 's are equal

What is the test statistic?

FBL=

(Round to two decimal places as needed.)

What is the p-value?

The p-value is .

(Round to three decimal places as needed.)

What is the correct conclusion?

A.

The blocking factor was not effective because H 0 was rejected.

B.

The blocking factor was effective because H 0 was rejected.

C.

The blocking factor was effective because H 0 was not rejected.

D.

The blocking factor was not effective because H 0 was not rejected.

c. If warranted, determine which pairs of flavors were different from one another using α=0.05.

Were flavors 1 and 2 preferred differently? Choose the correct answer below and, if necessary, fill in any answer boxes in your choice.

A.

The absolute sample mean difference of flavors 1 and 2 is nothing , which means the flavors were not preferred differently. (Round to two decimal places as needed.)

B.

The absolute sample mean difference of flavors 1 and 2 is nothing , which means the flavors were preferred differently. (Round to two decimal places as needed.)

C.

Multiple comparisons are not warranted.

Were flavors 1 and 3 preferred differently? Choose the correct answer below and, if necessary, fill in any answer boxes in your choice.

A.

The absolute sample mean difference of flavors 1 and 3 is nothing , which means the flavors were not preferred differently. (Round to two decimal places as needed.)

B.

The absolute sample mean difference of flavors 1 and 3 is nothing , which means the flavors were preferred differently. (Round to two decimal places as needed.)

C.

Multiple comparisons are not warranted.

Were flavors 1 and 4 preferred differently? Choose the correct answer below and, if necessary, fill in any answer boxes in your choice.

A.

The absolute sample mean difference of flavors 1 and 4 is nothing , which means the flavors were not

preferred differently. (Round to two decimal places as needed.)

B.

The absolute sample mean difference of flavors 1 and 4 is

nothing , which means the flavors were preferred differently. (Round to two decimal places as needed.)

C.

Multiple comparisons are not warranted.

Were flavors 2 and 3 preferred differently? Choose the correct answer below and, if necessary, fill in any answer boxes in your choice.

A.

The absolute sample mean difference of flavors 2 and 3 is nothing , which means the flavors were not

preferred differently. (Round to two decimal places as needed.)

B.

The absolute sample mean difference of flavors 2 and 3 is

nothing , which means the flavors were preferred differently. (Round to two decimal places as needed.)

C.

Multiple comparisons are not warranted.

Were flavors 2 and 4 preferred differently? Choose the correct answer below and, if necessary, fill in any answer boxes in your choice.

A.

The absolute sample mean difference of flavors 2 and 4 is nothing , which means the flavors were not preferred differently. (Round to two decimal places as needed.)

B.

The absolute sample mean difference of flavors 2 and 4 is nothing , which means the flavors were preferred differently. (Round to two decimal places as needed.)

C.

Multiple comparisons are not warranted.

Were flavors 3 and 4 preferred differently? Choose the correct answer below and, if necessary, fill in any answer boxes in your choice.

A.

The absolute sample mean difference of flavors 3 and 4 is nothing , which means the flavors were preferred differently. (Round to two decimal places as needed.)

B.

The absolute sample mean difference of flavors 3 and 4 is nothing , which means the flavors were not preferred differently. (Round to two decimal places as needed.)

C.

Multiple comparisons are not warranted.

At the .01 significance level, does the data below show significant correlation?

• Yes, significant correlation
• No

**Please explain why its yes/no

. A teaching assistant for Statistics course as a university collected data from students in her class to investigate whether study time per week (average number of hours) differed between students who planned to go to graduate school and those who did not. The data were as follows:

Graduate school: 15, 7, 15, 10, 5, 5, 2, 3, 12, 16, 15, 37, 8, 14, 10, 18, 3, 25, 15, 5, 5

No graduate school: 6, 8, 15, 6, 5, 14, 10, 10, 12, 5.

State the null and alternative hypotheses using statistical notations. Use R command t.test to test whether study time differed between two groups. Include your R output and identify the test statistic and p-value. Draw the conclusion.

The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 229 customers on the number of hours cars are parked and the amount they are charged. Number of Hours Frequency Amount Charged 1 18 $ 3 2 38 7 3 52 13 4 40 17 5 33 22 6 13 24 7 6 27 8 29 30 229 a. Convert the information on the number of hours parked to a probability distribution. (Round your answers to 3 decimal places.) Hours Probability 1 2 3 4 5 6 7 8 a-2. Is this a discrete or a continuous probability distribution? Discrete Continuous b-1. Find the mean and the standard deviation of the number of hours parked. (Do not round intermediate calculations. Round your final answers to 3 decimal places.) Mean Standard deviation b-2. How long is a typical customer parked? (Do not round intermediate calculations. Round your final answers to 3 decimal places.) The typical customer is parked for hours c. Find the mean and the standard deviation of the amount charged. (Do not round intermediate calculations. Round your final answers to 3 decimal places.) Mean Standard deviation

This information is for problems 7 – 14:
Two economics professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results:
                                                Mean Grade                      Standard Deviation
Professor Welker            83.6                                                        21.6
Professor Ackerman       79.7                                                        12.0
At the 0.01 level of significance, what is your conclusion?

This information is for problems 7 – 14:
Two economics professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results:
                                                Mean Grade                      Standard Deviation
Professor Welker            83.6                                                        21.6
Professor Ackerman       79.7                                                        12.0
At the 0.05 level of significance, what is your conclusion?

in Applied Business Research & Statistics, can you explain how the type of variable (qualitative and quantitative) and the level of measurement used influence the presentation of the data collected for the variable and the statistics that can be calculated for the variable. Can you provide your own examples?

A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows: Salary Education

a. Find the sample regression equation for the model: Salary = β0 + β1Education + ε. (Round answers to 2 decimal places.) Salaryˆ= + Education b. Interpret the coefficient for Education. As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $4,070. As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $8,590. As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $4,070. As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $8,590. c. What is the predicted salary for an individual who completed 6 years of higher education? (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.) Salaryˆ $