Plz use both pure NE and MIXED strategy (with Probability)

Consider a firm with two agents – 1 and 2. Both agents have to choose between two options: Client Focus or Cost Focus. If both choose Client the payoffs to 1 are 20 and 10 to agent 2. If both agents choose to play Cost the payoffs are 15 to agent 1 and 25 to agent 2, respectively. Finally, if any other combination of actions is chosen the payoffs to each agent are 0.

a. Assume that the agent choose their actions simultaneously. Draw the normal form of the game and derive all of the Nash equilibria.

b. Now assume that the game is played sequentially: Agent 1 makes her choice of action first, this is observed by Agent 2, who then makes his choice. Draw the extensive form of the game and find the subgame perfect equilibria. Briefly interpret this game in the context of: (i) leadership and corporate culture; and (ii) the Basic Value Maximisation Principle.

newspaper publisher is considering launching a new "national" newspaper in Anytown. It is believed that the newspaper would have to capture over 12% of the market in order to be financially viable. During the planning stages of this newspaper, a market survey was conducted of a sample of 400 readers. After providing a brief description of the proposed newspaper, one question asked if the survey participant would subscribe to the newspaper if the cost did not exceed $20 per month. Suppose that 58 participants said they would subscribe.

a. Can the publisher conclude that the proposed newspaper will be financially viable? Perform the appropriate test at a 1% level of significance.

b. Suppose the actual value of the overall proportion of readers who would subscribe to this newspaper is 0.13. Was the decision made in part (a) correct? If not, what type of error was made?

c. State the meaning of a Type I and Type II error in the context of this scenario. And what would be the repercussions of making these errors to the publisher?

An insurance company wants to monitor the quality of its procedures for handling loss claims from its auto insurance policyholders. Each month the company selects an SRS from all auto insurance claims filed that month to examine them for accuracy and promptness.

What kind of study was this?

A) Matched pairs experiment.   

B)Double blind experiment.

C) Observational Study.

D) Randomized comparative experiment.

*Please Explain*

A sample of 11 circuits from a large normal population has a mean resistance of 2.20 ohms. We know from past testing that the population standard deviation is 0.35 ohms.

1. Determine a 95% confidence interval for the true mean resistance of the population.

2. In part 1 above, do you need any assumptions, if yes what, if no why.

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. A simple random sample of 25 filtered 100 mm cigarettes is​ obtained, and the tar content of each cigarette is measured. The sample has a mean of 20.2 mg and a standard deviation of 3.81 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg, which is the mean for unfiltered king size cigarettes.

What are the​ hypotheses?

A. H0​: μ>21.1 mg

H1​: μ<21.1 mg

B.H0​: μ=21.1 mg

H1​: μ<21.1 mg

C.H0​: μ<21.1 mg

   H1​: μ ≥ 21.1 mg

D. H0​: μ =21.1 mg

H1​: μ ≥ 21.1mg

Identify the test statistic.

t = _________

Identify the​ P-value.

The​ P-value is ___________

State the final conclusion that addresses the original claim. Choose the correct answer below.

A. Fail to reject H0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

B. Reject H0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

C. Reject H0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

D.Fail to reject H0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

What do the results​ suggest, if​ anything, about the effectiveness of the​ filters?

A.The results suggest that the filters are effective.

B.The results suggest that the filtered cigarettes have the same tar content as unfiltered king size cigarettes.

C.The results do not suggest that the filters are effective.

D.The results suggest that the filters increase the tar content.

E.The results are inconclusive because the sample size is less than 30.

015824 A systems analyst tests a new algorithm designed to work faster than the currently-used algorithm. Each algorithm is applied to a group of 89 sample problems. The new algorithm completes the sample problems with a mean time of 17.64 hours. The current algorithm completes the sample problems with a mean time of 17.75 hours. Assume the population standard deviation for the new algorithm is 4.561 hours, while the current algorithm has a population standard deviation of 4.210 hours. Conduct a hypothesis test at the 0.05 level of significance of the claim that the new algorithm has a lower mean completion time than the current algorithm. Let μ1 be the true mean completion time for the new algorithm and μ2 be the true mean completion time for the current algorithm. Step 1 of 5: State the null and alternative hypotheses for the test.

Compare the coding techniques used in quantitative versus qualitative research

Please conduct an independent-sample t-test, α = .05.  

Two persons are arguing about the size of different breeds of dogs. One believes that German Shepherds are larger than Huskies, while the other person believes the opposite is true. So they conducted a study to see which one of them is correct by randomly sampling and weighting 10 dogs of each breed they saw on a Sunday afternoon in their community. This is an independent-sample case. The data are as follows:

German Shepherds: 55, 72, 61, 43, 59, 70, 67, 49, 55, 63

Huskies: 48, 77, 46, 51, 60, 44, 53, 61, 52, 41

Sky Kitchens is the second largest airline caterer in the United States, providing nearly all the meals for passengers of three major airlines and several smaller commuter airlines. As part of a total quality management (TQM) program, its largest airline client, Continental Airlines, has recently met with representatives of Sky Kitchens to discuss a customer satisfaction program that it is planning to implement. Continental plans to interview a sample of its customers four times a year. In the survey, it intends to ask customers to rate the quality of meals provided on a 1–10 scale, where 1 means poor and 10 means excellent. It has just completed a benchmark study of 1,000 customers. In that study, meals received an average rating of 8.7 on the 10-point scale, with a standard deviation of 1.65. Continental has indicated that it wants Sky Kitchens to guarantee a level of satisfaction of 8.5 in the first quarterly survey, to be conducted in three months. For its quarterly surveys, Continental plans to use a sample size of 500. In the new contract with Sky Kitchens, Continental wants to include a clause that will penalize Sky Kitchens $50,000 for each one-tenth of a point it falls below an average of 8.5 on the next survey’s satisfaction scale.

1. What is the 99.74% confidence interval (CI) for the true satisfaction level based on the benchmark survey?

2. What is the 99% confidence interval (CI) for the true satisfaction level based on the benchmark survey?

3. What is the 95.44% CI for the true satisfaction level based on the benchmark survey?

4. What is the 95% CI for the true satisfaction level based on the benchmark survey?

5. As Sky Kitchens, what do you think of Continental’s requirement for a level of satisfaction of 8.5 in the first quarter survey?

6. Assume that the upcoming 1st -quarter satisfaction survey shows anaverage rating of 8.4 on satisfaction with meals. Assume that the population standard deviation is1.65. Compute the 99% CI for the true satisfaction level based on the 1st-quarter survey. As Sky Kitchens, what is the best way to present and interpret the resulting CI?

7. If you were negotiating for Sky Kitchens, how would you respond to Continental regarding the penalty clause? Is there a better or more reasonable way to revise it

Suppose that a deck of 52 cards contains 26 red cards and 26 black cards. Say we use the 52 cards to randomly distribute 13 cards each among two players (2 players receive 13 card each).

a. How many ways are there to pass out 13 cards to each of the two players?

b. What is the probability that player 1 will receive 13 cards of one color and player 2 receive 13 cards of the other color?

The Sorry State Lottery requires you to select five different numbers from 0 through 63. (Order is not important.) You are a Big Winner if the five numbers you select agree with those in the drawing, and you are a Small-Fry Winner if four of your five numbers agree with those in the drawing. (Enter your answers as exact answers.)

What is the probability of being a Big Winner?

What is the probability of being a Small-Fry Winner?

What is the probability that you are either a Big Winner or a Small-Fry Winner?

Contracts for two construction jobs are randomly assigned to one or more of three firms A, B, and C. Let Y1 denote the number of contracts assigned to firm A and Y2 the number of contracts assigned to firm B. Recall that each firm can receive 0, 1 or 2 contracts.

(a) Find the joint probability function for Y1 and Y2.

(b) Find the marginal probability of Y1 and Y2.

(c) Are Y1 and Y2 independent? Why?

(d) Find E(Y1 − Y2).

(e) Find Cov(Y1, Y2)

Exercise 5a: What is the recommend number of classes for 1.5, 2.2, 3.4,3.4,3.4 ,4.5, 5.1?

Exercise 5b: What is a good class width?

Exercise 5c: Give the frequency distribution.

Exercise 5d. Make a list of the lower limits of all classes

Exercise 5e: Make two columns in Excel, one with all observations (1.5,2.2,...) and one with the lower limits. Delete the lowest number in the lower limit column. This is your bin column

.Exercise 5f: In the Excel Data Toolpak, choose histogram. Enter the numbers and the bins. Show the chart in your homework

Exercise 5g: Compare with the manual chart

A diagnostic test either provides a + result (has the disease) or - result (does not have the disease). 5% of the population has the disease. For a patient with the disease, 75% will test (+)/ 25% will test (-). For a patient that does not have the disease, 15 % will test (+)/ 85% will test (-).

Part A) If everyone in the population is tested, what proportion of the test results will be positive?

Part B) For a patient who gets a Positive result, what is the probability of having the disease?