Changes in Education Attainment: According to the U.S. Census Bureau, the distribution of Highest Education Attainment in U.S. adults aged 25 - 34 in the year 2005 is given in the table below.

Census: Highest Education Attainment - 2005

In a survey of 4000 adults aged 25 - 34 in the year 2013, the counts for these levels of educational attainment are given in the table below.

Survey (n = 4000): Highest Education Attainment - 2013

The Test: Test whether or not the distribution of education attainment has changed from 2005 to 2013. Conduct this test at the 0.01 significance level.(a) What is the null hypothesis for this test?

H₀: p₁ = p₂ = p₃ = p₄ = p₅ = 1/5 H₀: The probabilities are not all equal to 1/5.     H₀: p₁ = 0.14, p₂ = 0.48, p₃ = 0.08, p₄ = 0.22, and p₅ = 0.08. H₀: The distribution in 2013 is different from that in 2005.

(b) The table below is used to calculate the test statistic. Complete the missing cells.
Round your answers to the same number of decimal places as other entries for that column.

(c) What is the value for the degrees of freedom? 7
(d) What is the critical value of

χ²

? Use the answer found in the

χ²

-table or round to 3 decimal places.
t_α = 8

(e) What is the conclusion regarding the null hypothesis?

reject H₀ fail to reject H₀    

(f) Choose the appropriate concluding statement.

We have proven that the distribution of 2013 education attainment levels is the same as the distribution in 2005. The data suggests that the distribution of 2013 education attainment levels is different from the distribution in 2005.      There is not enough data to suggest that the distribution of 2013 education attainment levels is different from the distribution in 2005.

A team of ornithologists in southeast Peru is studying the relative (geographical) distributions of two subspecies of Rupicola peruvianus, R. p. saturatus and R. p. aequatorialis, in a forest where the ranges of the two overlap. In doing so, they set up an observation post in the forest and make observations for six days.

(a) It is determined that a reasonable probability model for the number of R. p. aequatorialis observed over this time is Poisson, with λ1 > 0 sightings on average. In terms of λ1, what is the probability that they have k sightings?

(b) It is further determined that the number of R. p. saturatus observed over the same time is independently Poisson, with λ2 > 0 sightings on average. What is the (probability) distribution of the total number of birds that will be sighted? Hint: the sum X + Y of two independent Poisson random variables X and Y is also a Poisson random variable. Furthermore, E(X + Y ) = E(X) + E(Y ).

(c) In terms of λ1 and λ2, what is the probability that the total number of birds sighted will be exactly n?

(d) Suppose that, at the end of the six days, the total number of birds that have been sighted is exactly n. Conditional on this event, what is the probability that exactly k of these n are R. p. aequatorialis? Hint: P(A|B) = P(A∩B) P(B)

(e) Conditional on the event of observing n birds in total, what is the (named) distribution of the number of R. p. aequatorialis? Hint: write the probability in part (d) in terms of λ1 λ1+λ2

11.)  

An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Assuming each simple event is as likely as any​ other, find the probability that the sum of the dots is greater than 2.

The probability that the sum of the dots is greater than 2 is

12.)

An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Find the probability of the sum of the dots indicated.

Getting a sum of 1

The probability of getting a sum equal to 1 is

13.)

An experiment consists of tossing 4 fair​ (not weighted)​ coins, except one of the 4 coins has a head on both sides. Compute the probability of obtaining exactly 1 headhead.

The probability of obtaining exactly 1 headhead is

15.)

An experiment consists of rolling two fair​ (not weighted) dice and adding the dots on the two sides facing up. Each die has the number 1 on two opposite​ faces, the number 2 on two opposite​ faces, and the number 3 on two opposite faces. Compute the probability of obtaining the indicated sum.

Sum of 8

The probability of getting a sum of 8 is nothing

16.)

An experiment consists of dealing 7 cards from a standard​ 52-card deck. What is the probability of being dealt exactly 1 ace​?

The probability of being dealt exactly1 ace is approximately

Answer the following questions about probabilities regarding the toss of two dice and their resulting sum. The table below lists all possible outcomes and will be helpful!
(a) (1 point) What’s the probability of rolling a sum that is anything other than 7?
(b) (1 point) What’s the probability of rolling a sum of that is greater than or equal to 8?
(c) (1 point) Given that Die 1 is a 5, what is the probability of rolling a sum of that is greater than or equal to 8?
(d) (1 point) What’s the probability of rolling a sum that is an odd number?
(e) (1 point) What’s the probability of rolling doubles? (Rolling doubles means both dice show the same number.)

Research and, in two paragraphs, describe the Michigan State Court system, from trial courts through the highest appellate level. You should cover the jurisdiction of each court, the length of the terms of judges on each court, and the number of judges who sit on panels to decide cases in the Michigan Court of Appeals and Supreme Court.

Suppose that MERCEDES COMPANY has announced that some of the cars that they sold( of each of the 3 MODELS X, Y and Z) in NORTH CYPRUS last year (2019) has turned out to be DEFECTIVE.

The respective number of Non- Defective and Total Number of Mercedes cars sold for each Model have been reported to be as follows;

                                                                                                                   MODEL

                                                                                                     X                  Y                    Z

   NUMBER OF NON DEFECTIVE CARS SOLD                     150               50               500

              TOTAL NUMBER OF CARS SOLD                            300              500               800

Suppose that we randomly select 2 different (First and Second) consumers each of whom purchased a new MERCEDES car in 2020. Given this experiment answer all of the following 10 questions.

Q1) What is the probability of the first consumer’s car to be MODEL X?

Q2)What is the probability of the first consumer’s car to be either MODEL Y or MODEL Z?

Q3)What is the probability of the second consumer’s car to be either MODEL X or MODEL Y?

Q4) What is the probability of the first consumer’s car to be either DEFECTIVE or MODEL Y?

Q5) What is the probability of the second consumer’s car to be either NON-DEFECTIVE or MODEL Z?

Q6)If the second consumer’s car is MODEL Y, what is the probability that İt is NON-DEFECTIVE?

Q7) If the first consumer’s car is NON-DEFECTIVE what is the probability that it is MODEL Z?

Q8) What is the probability of the cars of both of these 2 consumers to be DEFECTIVE?

Q9)If the car of the first consumer is MODEL Z what is the probability of the car of the second consumer to be MODEL X?

Q10) If the car of the second consumer is DEFECTIVE, what is the probability of the car of the first consumer to be MODEL Y?

Support department cost allocation

Hooligan Adventure Supply produces and sells various outdoor equipment. The Molding and Assembly production departments are supported by the Personnel and Maintenance departments. Personnel costs are allocated to the production departments based on the number of employees, and Maintenance costs are allocated based on number of service calls. Information about these departments is detailed in the following table:

1. Which of the following statements matches the sequential method of cost allocations?

a. Support departments are often allocated in order from lowest to the highest cost with preference given to the departments that serve few support departments and have no accurate cost drivers.

b. Support departments are often allocated in order from highest to lowest cost with preference given to the departments that serve many support departments and have accurate cost drivers.

c. The sequential method only allocates costs to departments that have a high profit margin.

d. None of the above.

Which department should be allocated first and identify the reason.

Reason:

a. It has the lowest departmental cost with no accurate cost driver

b. It has the highest departmental cost with no accurate cost driver.

c. It has the lowest departmental cost with an accurate cost driver.

d. It has the highest departmental cost with an accurate cost driver.

2. Based on your response in part (1), determine the total costs allocated from each support department to each production department using the sequential method.

3. Which allocation method is usually the most accurate?

a. Direct method.

b. Reciprocal method.

c. Sequential method.

d. None of the above.

What is a potential disadvantage of the reciprocal method?

a. It is the most complex method of cost allocation.

b. Both fixed and variable costs are allocated based on the computed cost base.

c. It considers the support department cost as its own department cost.

d. All the above.

4. (a) In a fraud detection system a number of different algorithms are working indepen- dently to flag a fraudulent event. Each algorithm has probability 0.9 of correctly detecting such an event. The program director wants to be make sure the system can detect a fraud with high probability. You are tasked with finding out how many different algorithms need to be set up to detect a fraudulent event. Solve the following 3 problems and report to the director. [Total: 18 pts] (b) Suppose n is the number of algorithms set up. Derive an expression for the probability that a fraudulent event is detected. (6 pts) (c) Using R, draw a plot of the probability of a fraudulent event being detected versus n, varying n from 1 to 10. (6 pts) (d) Your colleague claims that if the company uses n = 4 algorithms, the probability of detecting the fraudulent event is 0.9999. The director is not convinced. Generate 1 million samples from Binomial distribution with n = 4, p = 0.90 and count the number of cases where Y = 0. Report the number to the director. (6 pts)

Given a class Stack with the interface

   public void push(char n) // pushes n onto stack

   public char pop() // return the top of the stack, removing element from stack

   public boolean isEmpty() // return true if stack is empty

Write a method

public int removeX(Stack<Character> stack)

which takes a stack of Characters, removes the occurrences of ‘X’ and returns the count of the number of Xs removed. It must restore the stack to its original order (less the Xs). You may use any other internal storage you choose.

For example, input of stack

      Bottom [ A X B C X D] Top

Would return 2 and the stack would now be

       Bottom [A B C D] Top

Write a function called remove_punct() that accepts a string as a parameter, removes the punctuation (',', '!', '.') characters from the string, and returns the number of punctuation characters removed. For example, if the string contains ['C', 'p', 't', 'S', ',', '1', '2', '1', '.', 'i', 's', 'f', 'u', 'n', '!', '\0'], then the function should remove the punctuation characters. The function must remove the characters by shifting all characters to the right of each punctuation character, left by one spot in the string. This will overwrite the punctuation characters, resulting in: ['C', 'p', 't', 'S', '1', '2', '1', 'i', 's', 'f', 'u', 'n', '\0']. In this case, the function returns 3. Note: if the srtring does not contain any punctuation characters, then the string is unchanged and the function returns 0.

Please write in C