Maurice’s Pump Manufacturing Company currently maintains plants in Atlanta and Tulsa that supply major distribution centers in Los Angeles and New York. Because of an expanding demand, Maurice has decided to open a third plant and has narrowed the choice to one of two cities—New Orleans or Houston. The pertinent production and distribution costs, as well as the plant capacities and distribution center demands, are shown in the following table.

Plants			Distribution Centers
Location	Capacity	Production Cost (per unit)	LA	New York
Atlanta (existing)	600	$6	$8	$5
Tulsa (existing)	900	$5	$4	$7
New Orleans (Proposed)	500	$4 (anticipated)	$5	$6
Houston (Proposed)	500	$3 (anticipated)	$4	$6
Forecast Demand			800	1,200

Help the company decide which of the two proposed plant should be opened. Create a spreadsheet model of this situation and solve using Solver. Clearly show the values of the decision variables and the objective.

• Age at onset of dementia was determined in the general population to be m = 75.5 and s = 5.8.
• Based on the data above, what is the z score for the age of 72?

• Based on the data you have and the z table, what percentage of people might start to show signs of dementia at or before age 72? Note: DO NOT ROUND

An education researcher claims that 62% of college students work​ year-round. In a random sample of 200

college​ students, 124 say they work​ year-round. At alpha equals=0.010​, is there enough evidence to reject the​ researcher's claim?

A.) What is the critical value?

B.) What is the rejection region?

C.) What is the standardized test statistic z?

D.) Should the null hypothesis be rejected?

A chemical company produces two chemicals, denoted by 0 and 1, and only one can be produced at a time. Each month a decision is made as to which chemical to produce that month. Because the demand for each chemical is predictable, it is known that if 1 is produced this month, there is a 70 percent chance that it will also be produced again next month. Similarly, if 0 is produced this month, there is only a 20 percent chance that it will be produced again next month.

To combat the emissions of pollutants, the chemical company has two processes, process A, which is efficient in combating the pollution from the production of 1 but not from 0, and process B, which is efficient in combating the pollution from the production of 0 but not from 1.   Only one process can be used at a time. The amount of pollution from the production of each chemical under each process is

	0	1
A	100	10
B	10	30

Unfortunately, there is a time delay in setting up the pollution control processes, so that a decision as to which process to use must be made in the month prior to the production decision. Management wants to determine a policy for when to use each pollution control process that will minimize the expected total discounted amount of all future pollution with a discount factor of 0.5.

Suppose now that the company will be producing either of these chemicals for only 4 more months, so a decision on which pollution control process to use 1 month hence only needs to be made three more times.

a) Define Stage, states, and alternatives.

b) Formulate the cost matrix.

c) Identify the stationary policies.

d) Formulate the transition matrix.

e) Find an optimal policy for this three-period problem.

1. What is a monotone class?
2.Prove that every algebra or field is a monotone class

Proof that
1. show that the intersection of any collection of algebra or field on sample space is a field
2. Union of field may not be a field

Consider the following regression model: Yi = αXi + Ui , i = 1, .., n (2)

The error terms Ui are independently and identically distributed with E[Ui |X] = 0 and V[Ui |X] = σ^2 .

1. Write down the objective function of the method of least squares.

2. Write down the first order condition and derive the OLS estimator αˆ.

Suppose model (2) is estimated, although the (true) population regression model corresponds to: Yi = β0 + β1Xi + Ui , i = 1, .., n with β0 different to 0.

3. Derive the expectation of αˆ, E[ˆα], as a function of β0, β1 and Xi . Is αˆ an unbiased estimator for β1? [Hint: Derive first E[ˆα|X].]

4. Derive the conditional variance of αˆ, V[ˆα|X], as a function of σ^2 and Xi .

Table #10.1.6 contains the value of the house and the amount of rental income in a year that the house brings in ("Capital and rental," 2013). Find the correlation coefficient and coefficient of determination and then interpret both.

VALUE	RENTAL	VALUE	RENTAL	VALUE	RENTAL	VALUE	RENTAL
81000	6656	77000	4576	75000	7280	67500	6864
95000	7904	94000	8736	90000	6240	85000	7072
121000	12064	115000	7904	110000	7072	104000	7904
135000	8320	130000	9776	126000	6240	125000	7904
145000	8320	140000	9568	140000	9152	135000	7488
165000	13312	165000	8528	155000	7488	148000	8320
178000	11856	174000	10400	170000	9568	170000	12688
200000	12272	200000	10608	194000	11232	190000	8320
214000	8528	208000	10400	200000	10400	200000	8320
240000	10192	240000	12064	240000	11648	225000	12480
289000	11648	270000	12896	262000	10192	244500	11232
325000	12480	310000	12480	303000	12272	300000	12480

Dmitry suspects that his friend is using a weighted die for board games. To test his theory, he wants to see whether the proportion of odd numbers is different from 50%. He rolled the die 40 times and got an odd number 14 times.

Dmitry conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of odds is different from 50%

(a) H0:p=0.5H0:p=0.5; Ha:p≠0.5Ha:p≠0.5, which is a two-tailed test.

(b) Use Excel to test whether the true proportion of odds is different from 50% Identify the test statistic, z, and p-value from the Excel output, rounding to three decimal places.

1. A university wants to estimate the proportion of its students who smoke regularly. Suppose that this university has N = 30, 000 students in total and a SRSWOR of size n will be taken from the population. a) If the university wants the proportion estimator ˆp to achieve the precision with tolerance level e = 0.03 and risk α = 0.1. Estimate the minimal sample size needed for this estimation. (z0.1 = 1.28, z0.05 = 1.65) b) Suppose that, in a pilot study, the university takes a SRSWOR of size 20 students, among which only 2 students are found to be smokers. Based on this preliminary result, re-compute the minimal sample size for part (a). c) Suppose the university chooses the sample size estimated from (b), and finds that the sample proportion is ˆp = 0.15. Construct a 90% confidence interval for the population proportion p

One part of this question I am getting wrong. I'm assuming it's the test statistic? I got 1 for Question C, and I got 5.432 for question b, and I got B for question C.

An undergraduate student performed a survey on the perceived physical and mental health of UBC students for her term project. She collected information by asking students whether they are satisfied with their physical and mental health status. 129 male and 157 female UBC students were randomly chosen to participate in the survey. After finishing the survey, she presented the following tables in her term project paper.

For both sexes:

	Number of students
Perceived physical health, satisfied	229
Perceived physical health, not satisfied	57
Perceived mental health, satisfied	257
Perceived mental health, not satisfied	29

For male students:

	Number of students
Perceived physical health, satisfied	108
Perceived physical health, not satisfied	21
Perceived mental health, satisfied	110
Perceived mental health, not satisfied	19

For female students:

	Number of students
Perceived physical health, satisfied	121
Perceived physical health, not satisfied	36
Perceived mental health, satisfied	147
Perceived mental health, not satisfied	10

(a) To test independence of perceived physical health and sex, we want to use a chi-square model with  degree(s) of freedom.

(b) Compute the chi-square statistic used to test independence of perceived physical health and sex. Round your answer to 3 decimal places. For all intermediate steps, keep at least 6 decimal places.
Answer:

(c) Which of the following statements is correct based on the result of the Chi-square test?

A. At a 5% significance level, we reject the null hypothesis. There is strong evidence that perceived physical health and sex are associated.
B. At a 5% significance level, we do not reject the null hypothesis. There is little evidence that perceived physical health and sex are associated.
C. At a 5% significance level, we reject the null hypothesis. There is strong evidence that perceived physical health and sex are independent.
D. At a 5% significance level, we do not reject the null hypothesis. There is little evidence that perceived physical health and sex are independent.

or each of the following​ situations, find the critical​ value(s) for z or t.

​a)

H0​:

rhoρequals=0.50.5

vs.

HA​:

rhoρnot equals≠0.50.5

at

alphaαequals=0.010.01

​b)

H0​:

rhoρequals=0.40.4

vs.

HA​:

rhoρgreater than>0.40.4

at

alphaαequals=0.100.10

​c)

H0​:

muμequals=1010

vs.

HA​:

muμnot equals≠1010

at

alphaαequals=0.100.10​;

nequals=2626

​d)

H0​:

rhoρequals=0.50.5

vs.

HA​:

rhoρgreater than>0.50.5

at

alphaαequals=0.010.01​;

nequals=335335

​e)

H0​:

muμequals=2020

vs.

HA​:

muμless than<2020

at

alphaαequals=0.100.10​;

nequals=10001000

​a) The critical​ value(s) is(are)

▼

z*

t*

equals=nothing.

​(Use a comma to separate answers as needed. Round to two decimal places as​ needed.)

Select all of the true statements about the standard deviation of a quantitative variable.

1.The standard deviation of a group of values is a measure of how far the values are from the mean.

2.Changing the units of a set of values (e.g., converting from inches to feet) does not affect its standard deviation.

3.Standard deviation is resistive to unusual values.

4.The standard deviation of a set of values is equal to 00 if and only if all of the values are the same.

5.Standard deviation is never negative.

6.If a set of values has a mean of 00 and a standard deviation that is not 0,0, then adding a new data point with a value of00 will have no effect on the standard deviation.

Wildlife biologists inspect 158 deer taken by hunters and find 38 of them carrying ticks that test positive for Lyme disease.

a) Create a 90% confidence interval for the percentage of deer that may carry such ticks.

b) If the scientists want to cut the margin of error in half, how many deer must they inspect?

For a certain wine, the mean pH (a measure of acidity) is supposed to be 3.32 with a known standard deviation of σ = .14. The quality inspector examines 31 bottles at random to test whether the pH is too low, using a left-tailed test at α = 0.05.

(a) What is the power of this test if the true mean is μ = 3.30?

(b) What is the power of this test if the true mean is μ = 3.28?

(c) What is the power of this test if the true mean is μ = 3.26?

A medical researcher is studying the effects of a drug on blood pressure. Subjects in the study have their blood pressure taken at the beginning of the study. After being on the medication for 4 weeks, their blood pressure is taken again. The change in blood pressure is recorded and used in doing the hypothesis test.

Change: Final Blood Pressure - Initial Blood Pressure

The researcher wants to know if there is evidence that the drug increases blood pressure. At the end of 4 weeks, 35 subjects in the study had an average change in blood pressure of 2.1 with a standard deviation of 5.2.

Find the $p$-value for the hypothesis test.

Your answer should be rounded to 4 decimal places.