Exercise #6 (game theory and choice question) PLEASE TYPE OUT ANSWER

We are presented with land use choices. Individuals are free to choose their own development strategy based on the profit potential of the development

.

a) Does either landowner have a dominant strategy? (5 Points) A dominant strategy is what you are going to do, knowing what they are going to do—this leads to the Nash Equilibrium Explain how and what the dominant strategy is (hint, there does not need to be two dominant strategies).

b) Is there a Nash equilibrium? Explain. (5 Points)

d) What is the socially optimal solution? (5 Points)

e) How can we arrive at the optimal solution (consider the Coase Solution). Explain the necessary payoff. (5 Points)

Payoff Matrix

                                                                Davis

                                                                Alfalfa                                   Dairy Farm

                Apartment House             B: Profit =$700                 B: Profit = $400

                                                         D: Profit =$180                D: Profit = $425              

                Benson Commercial Real Estate           B: Profit =$650                 B: Profit = $455

                                                                                D: Profit =$400                D: Profit = $500              

I'm working on setting up a final project for Statistics and I wanted to make sure I am choosing the right test for my hypotheses. Are my test choices correct?

Hypotheses

1. I hypothesize that the difference in the respondent’s physical effort at work, and how difficult it is for the respondent to take time off, has an impact on the respondent’s general health.
   
   Statistical Test Used: ANOVA
   
2. I hypothesize that black men with less than college education are less likely to claim their workplace is safe and healthy than black men with a college education.
   
   Statistical Test Used: t-test
   
3. I hypothesize that the as the age of a respondent and if the workplace is safe and healthy has a significant impact on if the respondent reported back pain in the past 12 months.
   
   Statistical Test Used: Multiple Regression
   
4. I hypothesize respondents who reported trouble sleeping in the last 12 months have reported increasingly poor mental health in the past 30 days as the severity of days of trouble sleeping in the last 30 days increases. (ie. Sometime is less severe than Often)
   
   Statistics Test Used: Two Way ANOVA
   
5. I hypothesize that respondents that have reported they have been told they have diabetes and have been told they have depression are more likely to report poor general health.
   
   Statistical Test Used: Multiple Regression

Lab - Chapter 5 - Normal Distribution Problems

1. The machine that packages 5 lb. bags of sugar is designed to put an average (mean) of 5.1 lbs. with a standard deviation of 0.4 lbs. into the package.

a. What is the probability that a bag of sugar weighs less than 5 lbs.?

b. What is the probability that a bag of sugar weighs more than 5.1 lbs.?

c. What is the probability that a bag weighs between 4.5 and 5.5 lbs.?

d. What is the probability that a bag weighs between 5.4 and 6.6 lbs.?

2. A bag of individually wrapped candy claims to contain 45 pieces. The machine packaging the candy is designed to put an average of 43 pieces in the bag with a standard deviation of 4 pieces.

a. What is the probability that the bag has more than 45 pieces?

b. What is the probability that the bag has more than 51 pieces?

c. What is the probability that the bag contains between 43 and 47 pieces of candy?

d. What is the probability that the bag contains between 47 and 53 pieces of candy?

3. In recent years, the results of a particular college entrance exam showed an average score of 55 with a standard deviation of 4 points.

a. Based on these results, what is the probability that an incoming student scores below a 50?

b. What is the probability that a student scores above a 60?

c. What is the probability that a student scores between a 53 and a 59?

d. What is the probability that a student scores below a 58?

4. A bag of potato chips claims to contain 7 oz. of potato chips. Random sampling determines that the bags contain an average of 7.2 oz. with a standard deviation of 0.081 oz.

a. What is the maximum weight that 20% of the bags contain less than?

b. What is the minimum weight that the heaviest 15% of the bags contain?

c. In what weight interval are the middle 60% of the bags contained?

1) In a simple random sample of size 70, there were 35 individuals in the category of interest. It is desired to test H0 : p = 0.52 versus H1 : p < 0.52. Compute the test statistic z. 1) A) 2.37 B) 0.50 C) 0.06 D) -0.33

In a simple random sample of 1600 people age 20 and over in a certain​ country, the proportion with a certain disease was found to be 0.110 ​(or 11.0​%).

Complete parts​ (a) through​ (d) below.

a. What is the standard error of the estimate of the proportion of all people in the country age 20 and over with the​ disease? SE est=Answer______ (Round to four decimal places as​ needed.)

b. Find the margin of​ error, using a​ 95% confidence​ level, for estimating this proportion. m= Answer______ ​(Round to three decimal places as​ needed.)

c. Report the​ 95% confidence interval for the proportion of all people in the country age 20 and over with the disease.

The​ 95% confidence interval for the proportion is Answer (______, ______) ​(Round to three decimal places as​ needed.)

d. According to a government​ agency, nationally, 15.4% of all people in the country age 20 or over have the disease. Does the confidence interval you found in part​ (c) support or refute this​ claim? Explain.

The confidence interval supports this​ claim, since the value Answer ( ______ ) is contained within the interval for the proportion. ​(Type an integer or a decimal. Do not​ round.)

A mechanical engineering lab was hired to test the distance travelled by a new design of Dunlop brand golf balls, when struck by a standardized mechanically-driven club. Over several months of production, 30 randomly selected golf balls were tested. The mean distance travelled by the balls in the sample was 369 yards, and the standard deviation was 8.4 yards. Studies of pro golfers and their results have shown that balls that reach 350 yards in this test (not more, not less) are correlated with the best performance during matches. Report answers for multiple choice as a single letter with no punctuation, i.e. A

(1) What would the lab's null hypothesis be? A. The golf ball will travel 350 yards. B. The golf ball will travel a distance different from 350 yards. (2) Find the normalized tobs t o b s score for the observed mean distance travelled by Titleist. Report 2 digits after the decimal. tobs= t o b s =

(3) Sketch a normalized t distribution (see the Practice Problems for examples), and add tobs t o b s on the plot of the null t t -distribution. Shade in the appropropriate region that represents the probability of a value as large or more extreme that tobs t obs , in either direction. (I.e. don't forget the other tail.) You next find that for this sample, tcrit=t0.05(2),df t c r i t = t 0.05 ( 2 ) , d f = 2.04. Add this value to your t t distribution plot. Which of the following graphs most resembles your sketch?

(4) Find the 95% confidence interval for the mean distance travelled by Dunlop golf balls when hit by the mechanical golf club. Report 1 digit after the decimal for each value. 95% confidence interval: \[,\]

(5) What statistical conclusion should the researchers arrive at from this study? A. Reject the Null Hypothesis. B. Fail to Reject the Null Hypothesis. C. Accept the Null Hypothesis.

(6) What more colloquial conclusion should the researchers arrive at from this study? A. Golf balls from this brand do not travel the 350 yard target distance. B. The data does not provide evidence that this brand's golf clubs produce a distance other than 350 yards. C. The brand's golf balls travel on average 350 yards. Previous Page Next Page

Elementary Statistics (7th edition)

Chapter 8

review question 7

For Exercises 1 through 20, perform each of the following steps.

1. State the hypotheses and identify the claim.
2. Find the critical value(s).
3. Compute the test value.
4. Make the decision.
5. Summarize the results

7. Weights of Men’s Soccer Shoes Is lighter better? A random sample of men’s soccer shoes from an inter-national catalog had the following weights (in ounces).

At α=0.05, can it be concluded that the average weight is less than 10 ounces? Assume the variable is normally distributed.

you have a full factorial design with two levels for three factors. every trial had 2 runs. the difference in response values for every trial were [2,5,4,3,2,3,4,5]. calculate standard error for the effects.

how to do this? I tried lots of times.

Please state the step number next to the answer given, thank you!

A medical researcher believes that a drug changes the body's temperature. Seven test subjects are randomly selected and the body temperature of each is measured. The subjects are then given the drug, and after 30 minutes, the body temperature of each is measured again. The results are listed in the table below. Is there enough evidence to conclude that the drug changes the body's temperature?

Let d=(body temperature before taking drug)−(body temperature after taking drug)d=(body temperature before taking drug)−(body temperature after taking drug). Use a significance level of α=0.05 for the test. Assume that the body temperatures are normally distributed for the population of people both before and after taking the drug.

Step 1 of 5: State the null and alternative hypotheses for the test.
Step 2 of 5: Find the value of the standard deviation of the paired differences. Round your answer to two decimal places.
Step 3 of 5: Compute the value of the test statistic. Round your answer to three decimal places.
Step 4 of 5: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.
Step 5 of 5: Make the decision for the hypothesis test. (Reject or Fail to Reject)

1. Suppose we have the following information on GMAT scores for business and non-business majors:

Business Majors                      Non-Business Majors

n₁ = 8                                       n₂ = 5

_                                              _

X₁ = 545                                  X₂ = 525

s₁ = 120                                   s₂ = 60

a. Using a 0.05 level of significance, test to see whether the population variances are equal. (4 points)

b. Using a 0.05 level of significance, test the clam that average GMAT scores for business majors is above the average GMAT scores for non-business majors in the population. Assume unequal population variances.

1. We want to test to see whether average SAT scores for science majors equals the average SAT scores for non-science majors. We collect the following sample SAT scores:

Science            Non-Science

440                  1000

1550                1010

1400                970

370                  1020

600                  980

800                  1000

1390                1080

1100   

1500   

1480   

450     

1430   

Use Excel to test this hypothesis at the 0.05 level by first testing variances (at the 0.05 level) and then means. Submit your Excel file along with your explanation.

The price of a head of iceberg lettuce varies greatly with the season and the geographic location of a store. During February, a researcher contacts a random sample of 39 grocery stores across Canada and asks the produce manager of each to state the current price charged for a head of iceberg lettuce. Using the researcher’s results that follow, construct a 99% confidence interval to estimate the mean price of a head of iceberg lettuce in February in Canada.