1. In class, relevant to gerrymandering, I talked about the game of Divide and Choose. There’s a pile of goodies. Little Annie divides the big pile into two piles. Then Little Bobby chooses which of the two piles he wants, and Annie gets the other. The advantage of the method is that both children can see to it that they don’t envy what the other child gets. Annie can divide the big pile into two piles of equal value to her, and Bobby can choose the one he likes better, and neither can complain.

If the cake is worth 100 total to both, and the icing is worth 0 to Annie and 50 to Bobby, then Annie can do this:

Pile 1: all the icing, and 26% of the cake      Value to Annie 26. <----------

Value to Bobbie 76

Pile 2: no icing,and 74% of the cake             Value to Annie 74

Value to Bobbie 74. <------------ (this arrow is supposed to be connected to the above arrow)

Bobby will choose pile 1 because 76 is better than 74 (arrows). Bobby will get 76, and she’ll get pile 2 and get 74. (They’ll get the outcomes I put in bold.)

What would each get if Annie put half the icing and half the cake in each pile? Is that outcome Pareto efficient?

2. I’ll talk more about voting soon, but here’s something you can answer now. Let’s assume that there are exactly four candidates B, C, R and T in a primary election, and there are exactly four citizens voting on them. The citizens rank the four candidates starting from their favorite on the left to their least favorite on the right. So Citizen 1 prefers T to R to C to B.

Citizen 1.   T, R, C, B            

Citizen 2.   B, T, C, R

Citizen 3.   B, T, R, C

Citizen 4.   C, T, R, B

Which candidates are Pareto efficient for these four citizens? If a candidate is not Pareto efficient say why. (Hint: as usual, to decide whether a candidate is PE, look for another candidate that everyone prefers (“everyone”!).)

A business researcher wants to estimate the average travel time to work in Cleveland. A random sample of 45 Cleveland commuters is taken and the travel time (in minutes) to work is obtained from each. The data is shown in the table below.

1. Define the random variable X in words ________________________________________________
2. Calculate                      X   =     ___________ _Answer
3. Calculate                      sx =     ___________ _Answer
4. You wish to construct a 95% confidence interval for the population mean Cleveland commute time.
   1. Should you use a t-distribution or a z-normal distribution for this confidence interval?

                                                                      ____________________________ _Answer

2. Construct a 90% confidence interval for the population mean commute time.

                                                                                                                                                                                                                                    __________ <   µ   <   _________ _Answer

To study its performance, a newly designed motorboat was timed over a marked course under various wind and water conditions. Assuming that the necessary conditions can be met, use the following data (in minutes) to test at the 0.05 level of significance whether the difference among the three samples' means is significant.

SSTr = 85.53 and SSE = 140.20

1. Data from three hospitals show the number of surgeries performed on Monday thru Friday. At the 0.05 significance level, can we conclude there is a difference in the mean number of surgeries performed by hospital or by the day of the week?

please show work clearly.

Assignment
(1). In a city 25% of the people reads punch newspaper, 20% reads guidance. newspaper, 13% reads times newspaper, 10% reads both punch and guidance , 8% reads punch and time and 4% reads all three. If a person from this city is selected at random, what is the probability that he or she does not read any of this papers?
(2). In a community 32% of the population are male cassava farmers and 27% are female cassava farmers. what percentage of this community are cassava farmers?

A medical supply firm wishes to compare the mean daily output of its three plants in Toledo, Ohio; Ottumwa, Iowa; and Crab Apple Cove, Maine. Data were collected (measured in hundreds of units) for each site and are listed here.

Toledo:                       10        12        15        18        9          17        15        12        18

Ottumwa:                   15        17        18        12        13        11        12        11        12

Crab Apple Cove:    12        17        15        15        18        12        13        14        14

a. For each of the three plants, calculate the sum of the squared deviations around the mean of that plant.

b. Ignore the plant information (consider the data set, one sample with 27 observations). Calculate the sum of squared deviations around the mean of that group.

c. At the 10 percent level of significance, test to see if there is a difference in the means of the three plants.

QUESTION 4: (a) Briefly explain the process of launching an initial public offer of a new company that is now listing on the Ghana Stock Exchange.

b) What are three main functions of the investment bank in the IPO process?

c) What are three main differences between bonds and common shares or stocks?

d) What are three main differences between ordinary and preferred shares?

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

It is estimated that 3.5% of the general population will live past their 90th birthday. In a graduating class of 759 high school seniors, find the following probabilities. (Round your answers to four decimal places.)

(a) 15 or more will live beyond their 90th birthday


(b) 30 or more will live beyond their 90th birthday


(c) between 25 and 35 will live beyond their 90th birthday


(d) more than 40 will live beyond their 90th birthday

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

Ocean fishing for billfish is very popular in the Cozumel region of Mexico. In the Cozumel region about 47% of strikes (while trolling) resulted in a catch. Suppose that on a given day a fleet of fishing boats got a total of 27 strikes. Find the following probabilities. (Round your answers to four decimal places.)

(a) 12 or fewer fish were caught


(b) 5 or more fish were caught


(c) between 5 and 12 fish were caught

Based on long experience, an airline found that about 6% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline overbooks this flight by selling 263 ticket reservations for an airplane with only 255 seats.

(a) What is the probability that a person holding a reservation will show up for the flight?


(b) Let n = 263 represent the number of ticket reservations. Let r represent the number of people with reservations who show up for the flight. What expression represents the probability that a seat will be available for everyone who shows up holding a reservation?

P(r ≥ 263)P(r ≤ 263)    P(r ≥ 255)P(r ≤ 255)

(c) Use the normal approximation to the binomial distribution and part (b) to answer the following question: What is the probability that a seat will be available for every person who shows up holding a reservation? (Round your answer to four decimal places.)

One environmental group did a study of recycling habits in a California community. It found that 74% of the aluminum cans sold in the area were recycled. (Use the normal approximation. Round your answers to four decimal places.)

(a) If 384 cans are sold today, what is the probability that 300 or more will be recycled?


(b) Of the 384 cans sold, what is the probability that between 260 and 300 will be recycled?

- Second, suppose that you are the manager of a store that sells medical supplies for the handicapped or infirm. You see three major sources of conflict at the store: (1) many of the staff members who work the front desk do not like one another, (2) those who stock the shelves and work with the customers are resentful that they are not paid more, and (3) all employees are required to work nights and weekends, which cuts into their family and personal time.

Explain how you would manage any two of the three sources of conflict.

(answer in paragraph)

A college dean is interested in the exam performance of students in a biology course. After the final exam, students are randomly selected from three different section of the biology course. What can be conclude with an α of 0.05? The data are below.

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
η² =  ;  ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

At least on section differs on the final exam.None of the sections differ on the final exam.    

e) Conduct Tukey's Post Hoc Test for the following comparisons:
1 vs. 2: difference =  ; significant:  ---Select--- Yes No
2 vs. 3: difference =  ; significant:  ---Select--- Yes No

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
2 vs. 3: test statistic =  ; significant:  ---Select--- Yes No
1 vs. 2: test statistic =  ; significant:  ---Select--- Yes No