Income inequality and the poverty rate The following table summarizes the income distribution for the town of Perkopia, which has a population of 10,000 people. Every individual within an income group earns the same income, and the total annual income in the economy is $500,000,000. Suppose that in 1998, the poverty line is set at an annual income of $30,000 for an individual. Year Share of Total Income in Perkopia (Percent) Lowest Quintile Second Quintile Middle Quintile Fourth Quintile Highest Quintile 1998 5.0 11.0 16.0 24.0 44.0 2004 3.9 9.7 15.2 22.6 48.6 2010 3.5 8.8 14.7 22.0 51.0 2016 3.0 8.6 14.0 21.5 52.9 The data in the table suggest that there was income inequality from 1998 to 2016. Complete the following table to help you determine the poverty rate in Perkopia in 1998. To do this, begin by determining the total income of all individuals in each quintile using the fact that total annual income in the economy is $500,000,000. Next, determine the income of an individual in each quintile by dividing the total income of that quintile by the number of people in that quintile. (Hint: Recall that Perkopia has a population of 10,000 people.) Finally, determine whether the individual income for each quintile falls below the poverty line of $30,000. Quintile Share of Income in 1998 Total Income Individual Income Below Poverty Line? (Percent) (Dollars) (Dollars) Lowest 5.0 Second 11.0 Middle 16.0 Fourth 24.0 Highest 44.0 Using the information in this table, the poverty rate in Perkopia in 1998 is . Suppose that the government introduces a welfare program in which any individual with an income of less than $30,000 per year receives a lump-sum transfer payment of $5,000 from the government. Assume that, in the short run, there is no change in labor-supply behavior among the people in Perkopia. In the year 1998, the poverty rate after the introduction of the welfare program in Perkopia is . Again, suppose the government introduces a welfare program in which any individual with an income of less than $30,000 receives a lump-sum transfer payment of $5,000 from the government. Kate, a resident of Perkopia who currently earns an income of $29,578, has the opportunity to work overtime and earn an additional $1,900 this year. Which of the following statements are correct? Check all that apply. Kate may accept the overtime if she feels that taking it will increase the chances of her receiving a significant promotion. The $5,000 in aid presents a disincentive for Kate to make more than $30,000 per year. Kate would gain more income by turning down the overtime than she would if she accepted the overtime

The Stone Lion, a bed and breakfast located in a sleepy town, caters to two groups of customers, young couples interested in something marginally more exotic than a staycation, and corporate clients interested in doing some team-building at a location with no cellular service. Corporations know they can get rooms with minimal notice, but young couples on tight budgets tend to plan well in advance of their planned stay at the property. The corporate rate for rooms is $250 per person and the demand pattern is normal with a mean of 20 and a standard deviation of 10. The

proprietor of the Stone Lion takes pity on the young couples and charges them only $150 for identical accommodations.

I. How many rooms should be reserved for corporate clients?

II. If the price young couples are willing to pay increases by 50%, how many rooms should be reserved for corporate clients?

II. If the corporate demand and standard deviation both decrease by 50%, how many rooms should be reserved for corporate clients?

IV. What is the difference in the number of rooms that should be held by the Stone Lion if the standard deviation of corporate demand increases by five and if it decreases by five? 

V. If the corporate price and young couples' price both double, how many additional rooms should the Stone Lion hold for corporate clients?

The town of KnowWearSpatial, U.S.A. operates a rubbish waste disposal facility that is overloaded if its 5055 households discard waste with weights having a mean that exceeds 26.96 lb/wk. For many different weeks, it is found that the samples of 5055 households have weights that are normally distributed with a mean of 26.64 lb and a standard deviation of 12.56 lb.

What is the proportion of weeks in which the waste disposal facility is overloaded?
P(M > 26.96) =
Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Is this an acceptable level, or should action be taken to correct a problem of an overloaded system?

• No, this is not an acceptable level because it is not unusual for the system to be overloaded.
• Yes, this is an acceptable level because it is unusual for the system to be overloaded.

9) In a sample of 400 people selected randomly from one town, it is found that 130 of them are Gamecock Fans. At the 0.05 significance level, test the claim that the proportion of all people in the town who are Gamecock fans is 27%.

A] What type of statistical test can be used here?

a. Z-test of proportions            c. F Test                                e. Either c² or λ Test

b. a-Test of proportions           d. Either T or F-Test               f. T-Test

         ➔       

B] What is the stated claim about the proportion?

a. p = 0.27 The population proportion is the same as 27%.

b. p ≠ 0.27 The population proportion is different from 27%.

c. p > 0.27 The population proportion is greater than 27%.

d. p < 0.27 The population proportion is less than 27%.

e. p ≥ 0.27 The population proportion is greater than or equal to 27%.

f. p ≤ 0.27 The population proportion is less than or equal to 27%.

          ➔       

C] What are the null hypothesis (H₀) and the alternative hypothesis (H_a)? Circle one answer out of the “a” through “f” choices below.

                                    a. H₀: p > 0.27                           d. H_a: p < 0.27  

H_a:p ≤ 0.27                                     H₀: p ≥ 0.27

b. H₀: p = 0.27                           e. H_a: p = 0.27  

H_a: p ≠ 0.27                                   H₀: p ≠ 0.27

c. H_a: p > 0.27                            f. H₀: p < 0.27  

H₀: p ≤ 0.27                    H_a: p ≥ 0.27

                                                                                                                  ➔       

(9 continued)

D] Is this test:       a. Fat tailed?                          d. Inverse tailed?

b. Two tailed?                        e. Left tailed?

c. Right tailed?                       f. Meta-tailed?

          ➔       

E] What is the numerical value of the test statistic (TS) calculated from the observed data?

a. 0.5558          b. 2.4777     c. 1.9600     d. 2.0917     e. 0.6456     f. 0.6234

               ➔       

F] Provide EITHER the Critical Value (CV) OR the p-value

Critical Value (CV):

a. z = 2.05       b. z = 1.643 c. z = 1.96 d. z = 1.645         e. z = 2.576           f. z = 2.03

       ➔       

P-value:

a. 0.4210         b. 0.6830     c. 0.0132   d. 0.5321            e. 0.6283              f. 0.5221

       ➔       

G] For this problem about Gamecock fans, what is your decision about H₀ (the null hypothesis)?

a. Fail to reject the claim         c. Fail to reject H₀                   e. Accept H₀        

b. Reject H₀                           d. Reject the claim         f. Accept the claim

          ➔       

(9 continued)

H] For this problem about Gamecock fans, what is the decision about the original claim?

a. At the 5% level, there is NOT enough evidence to reject the claim that the proportion is 27%.

b. At the 10% level, there is enough evidence to reject the claim that the proportion is 27%.

c. At the 5% level, there is enough evidence to reject the claim that the proportion is 27%.

d. At the 10% level, there is NOT enough evidence to reject the claim that the proportion is 27%.

e. At the 5% level, there is enough evidence to support the claim that the proportion is 27%.

f. At the 10% level, there is enough evidence to support the claim that the proportion is 27%.

➔       

A certain restaurant in town is known for refusing to give separate bills to customers. After a group has ordered and eaten together at this restaurant, the group is presented with a single bill for the entire amount that the group has eaten. It has been suggested that the restaurant does this because, with a single bill, those who dine in groups will be more likely to simply divide the charge equally, each person paying the same amount irrespective of who ordered the most, and that diners, knowing they will ultimately divide the charge equally, will order more than they would have ordered had each expected to pay only for his own order. Analyze this situation using the following model.

There are 3 diners in a group, denoted i = 1, 2, 3. Each has a utility function of the form ui (xi , ci) = ai ln (xi) - ti , where xi represents the amount of food ordered and eaten by i and ti is the amount that i has to pay. The price of food is px = 1. Assume that a1 = 1, a2 = 2 and a3 = 3.

a. How much food will each individual order knowing that the bill will be shared and how much will they order in total?  

b. How much food will each individual order if he or she has to pay for her own order and how much will they order in total?

c. Provide an intuition for why the bill is larger in (a) than in (b).

(this is edited w; variables now)

You are a contractor on a $45 million project in down town Los Angeles. The project is scheduled to be completed in 2 years. You are 6 months into the project so far and project performance reports indicate that the budget has been exceeded by 10% thus far. Your schedule has also been delayed by more than a month due to subcontractor issues and labor disagreements. As a result, the quality of the job is suffering. It is your job as the Project Manager to get the project back on budget and schedule and address any quality issues. What steps will you take in order to get the job back on track? Identify actions that you could take and analyze which ones might work best.

Solve in EXCEL FORMAT, step by step.

A candidate for mayor in a small town has allocated $40,000 for last-minute advertising in the days preceding the election. Two types of ads will be used: radio and television. Each radio ad costs $200 and reaches an estimated 3,000 people. Each television ad costs $500 and reaches an estimated 7,000 people. In planning the advertising campaign, the campaign manager would like to reach as many people as possible, but she has stipulated that at least 10 ads of each type must be used. Also, the number of radio ads must be at least as great as the number of television ads. How many ads of each type should be used? How many people will this reach?

thank you!

A study is performed in a large southern town to determine whether the average amount spent on fod per four person family in the town is significantly different from the national average. Assume the national average amount spent on food for a four- person family is $150.

A what is the null and alternative hypothesis?

b. Is the sample evidence significant? significance level?

A researcher claims the mean age of residents of a small town is more than 38 years. The age (in years) of a random sample of 30 sutdents are listed below. At alpha=0.10, is there enough evidence to support the researcher's claim? assum the population standard deviation is 9 years.

Ages (in years)
41
33
47
31
26
39
19
25
23
31
39
36
41
28
33
41
44
40
30
29
46
42
53
21
29
43
46
39
35
33
42
35
43
35
24
21
29
24
25
85
56
82
87
72
31
53
31
33
54
60
31
81
32
40
26
52
37
71

a) Identify the claim and state Ho and Ha
(b) Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed and whether to use a z-test, a t-test, or a chi-square test. Explain your reasoning
(c)Choose one of the options Option 1: Find the critical value(s), identify the rejection region(s), and find the appropriate standardized test statistic. Option 2: Find the appropriate standardized test statistic and the P-value
(d) Decide whether to reject or fail to reject the null hypothesis
(e) Interpret the decision in the context of the original claim.

Suppose Rialto is the only movie cinema in a small college town, so it is essentially a monopoly for the local movie market. They charge a certain price P for a monthly pass. There is an overall demand curve for movie passes, given by P=900−4Q However, demand in the town has two distinct consumer groups: adults (A) and students (S). The demand for the whole group of adults is given by P=1200−8QA and the inverse demand for students is given by P=400−2QS Assume for simplicity that the constant marginal cost MC(Q) of showing a movie is 20 and there are no additional fixed costs.

(a) Suppose everybody can easily get a fake student ID and there is no way for UMovie to differentiate one group of consumers from another. As a result, the cinema is forced to charge a single price for both groups. Depict this in a figure.

(b) Compute the optimal quantity and price charged by UMovie, as well as total costs and profits. Under this price, who will go to movies? Remember the firm's production rule. Show these values in the figure.

(c) Suppose UMovie has spent $M > 0 to install a machine that can detect very accurately whether a student ID is fake. As a result, the cinema is able to charge each group a different price. Compute the optimal prices for the two groups of consumers.

(d)Depict the demand curve of each group of consumers in a diagram (the same or two different).