Directions: Use the Chi-Square option in the Nonparametric Tests menu to answer the questions based on the following scenario. (Assume a level of significance of .05 and use information from the scenario to determine the expected frequencies for each category) During the analysis of the district data, it was determined that one high school had substantially higher Graduate Exit Exam scores than the state average and the averages of high schools in the surrounding districts. To better understand possible reasons for this difference, the superintendent conducted several analyses. One analysis examined the population of students who completed the exam. Specifically, the superintendent wanted to know if the distribution of special education, regular education, and gifted/talented test takers from the local high school differed from the statewide distribution. The obtained data are provided below.

Number of students from the local high school who took the graduate exit exam - Special education - 16; Regular education - 90; Gifted/talented 16

Percent of test taking students statewide who took the Graduate Exit Exam - Special education 8%; Regular Education 79%; Gifted/Talented 13%

1. If the student distribution for the local high school did not differ from the state, what would be the expected percentage of students in each category?

2. What were the actual percentages of local high school students in each category? (Report final answer to two decimal places)

3. State an appropriate null hypothesis for this analysis.

4. What is the value of the chi-square statistic?

5. What are the reported degrees of freedom?

6. What is the reported level of significance?

7. Based on the results of the one-sample chi-square test, was the population of test taking students at the local high school statistically significantly different from the statewide population?

8. Present the results as they might appear in an article.

Assignment 4: T test for Dependent samples

Directions

Conduct a T test for Dependent Samples to answer the questions based on the following scenario. (Assume a nondirectional research hypothesis (two-tailed test) and a level of significance of .05)

Scenario

To further examine the school performance scores of the district, the superintendent identified schools within the district that could be matched to schools from surrounding districts using a series of demographic characteristics such as size, socio-economic status, and percent special education students. The data that were collected are presented below.

Questions

1. What are the mean school performance scores for the superintendent’s district and matched schools?
2. What are the standard deviations of the school performance scores for the superintendent’s district and matched schools?
3. State an appropriate null hypothesis for this analysis.
4. What is the observed or computed value of t?
5. What is the value of the degrees of freedom that are reported in the output?
6. What is the reported level of significance from the T Test for Dependent Means?
7. Based on the results of the T Test for Dependent Means, what would you conclude about the difference in scores of schools in the superintendent’s district and the matched schools?
8. Present the results as they might appear in an article. This must include a table and narrative statement that reports the results of the T Test for Dependent Means.

Note: The table must be created using your word processing program. Tables that are copied and pasted from SPSS are not acceptable.

Illinois State is worried about the rise in crimes in the state. The State Crime Control Unit engaged the services of a researcher to identify the factors that are contributing to rise in crime in the state. The researcher collected data for 50 cities within Illinois to ascertain the cause of rising crime. She collected data on seven variables including overall crime rate per 1 million residents in each of the 50 cities and reported violent crime rate per 100,000 residents.

The details of variables on which she collected data are as following.

1. provide interpretation for following:

R²:

Adjusted R²:

Coefficient of Funding:

Coefficient of undergraduate:

Standard Error of Estimate:

A study finds that graduate students send a mean of 74 text messages per day with a standard deviation of 15.2 text message per day while undergraduate students send a mean of 116 text messages per day with a standard deviation of 26.51. Which group, the undergraduate students or the graduate students have more variation in the number of sent text messages?

Lenny is an elementary school principal. He's concerned about how the families at his school are doing currently, so he creates a list of questions to ask some of them to get an idea of how they're holding up.

Match each scenario below with the correct sampling technique.

Consider the problem of school officials trying to identify cases of child abuse. In one community, officials believe that 3 percent of the area’s 10,000 children enrolled in public grade schools are physically abused. Measures can be taken to help these students, but first they must be located and identified. A preliminary screening program is proposed, whereby officials will contact and interview parents whenever evidence of abuse (such as unusual bruises) is found. Of course, screening is not entirely reliable. Although ninety-five (95) percent of abused children will be identified, it is estimated that screening will incorrectly label non-abused children as abused in 10 percent of the cases. School officials are anxious to identify cases of abuse, but they must proceed cautiously given the enormous stigma of charging someone with child abuse and the risk of liability to school officials if such an accusation is proven false. a. Construct the 2 X 2 contingency table corresponding to the child’s true condition (abused versus not abused) and the results of the screening test. b. Compute all of the marginal probabilities associated with this table. c. Compute all of the conditional probabilities associated with this table. d. Compute all of the joint probabilities associated with this table. e. What is the probability that a child enrolled in grade school is abused? f. What is the probability that an abused child will have a negative screen? g. If school officials decide to implement the screening program, what is the probability that they will make an error? h. Draw a reasonable decision tree that represents the school officials’ decision. Include the basic decision as well as uncertainties, probabilities, outcomes, and values associated with each alternative. If you do not have numeric estimates to complete the tree, describe the desired value in words or mathematical notation. (Note: You do not have enough information to solve the tree, so don’t even try!)

Should Parents Pay Their Children When They Earn High Grades in School?

We all probably recall knowing someone in school who got $5 for every “A” they earned in school. Research has found that encouragement of autonomous functioning, individual challenge, and positive feedback stimulates an intrinsic motivation to achieve (Deci & Ryan, 1985). If the environment is highly controlling, however, the internal forces for mastery-achievement may be undermined. Parents who use surveillance and frequent rewards socialize their children to be motivated by, and desire, extrinsic rewards. Two specific parenting behaviors were related to extrinsic motivation and lower school performance. They found that over controlling parents (those who engaged in extreme supervision of homework completion) had children who were more likely to rely on external sources for evaluation. Their grades and achievement scores were lower as well. Parents who relied on external rewards also had children with extrinsic motivation and lower school performance. Ginsburg and Bronstein speculate that extrinsically rewarded children use external criteria to assess their performance, which alters the children’s perception of themselves. This may undermine their ability to self-regulate and choose appropriate work. These children do not learn how to judge their own performance. Encouragement of intrinsic motivation, which is bidirectional and reciprocal, will foster independent self-evaluation and academic success. The goal is for the child to develop the ability to self-regulate and take responsibility for academic success; thus, the parents are not solely responsible for their child’s outcome. So, does paying our children for good grades motivate them to do well in school? Do you see how these children are not able to learn how to judge their own performance? Elaborate. What are some ways that parents can foster the development of intrinsic motivation?

BUSINESS DECISION: ADMINISTERING A GOVERNMENT PROGRAM

According to the Food and Nutrition Service of the U.S. Department of Agriculture, in one school year the National School Lunch Program served 31.2 million school lunches. Of these, 16.1 million students received free lunches, 3.2 million received lunches at a reduced price, and 11.9 million paid full price for their lunches.

The federal government reimburses school districts $2.99 for each free lunch, $2.29 for each reduced-price lunch, and $0.25 for each paid lunch. In addition to cash reimbursements, schools are entitled to receive USDA foods called "entitlement" foods at a value of 19.50 cents for each lunch served.

You are the administrator in charge of the school lunch program for your school district. Last month the schools in your district served 25,000 free lunches, 15,000 "reduced price" lunches, and 60,000 regular priced lunches.

a. Calculate the amount of reimbursement you expect to receive from the NSLP for last month.

b. In addition to the lunch reimbursement, the NSLP program pays your district $0.045 per one-half pint of milk served with each meal. If each student averaged 1 one-half pint of milk per meal, calculate the total amount of milk reimbursement you expect for last month.

c. The Bottom Line − What is the total amount of reimbursement your district will receive for last month?

d. Red Tape − The government paperwork you must submit requires that you report the average reimbursement per student for both lunch and milk combined last month. Calculate this amount. Round to the nearest cent.

*I have gotten that $1.29 is the correct answer for d, yet I cannot get the right answers for the first three questions*

1. Write the set { x | x ∈ R, x2 = 4 or x
2 = 9} in list form.
2. {x: x is a real number between 1 and 2} is an
a) finite set
b) empty set
c) infinite set
3. Write set {1, 5, 15, 25,…} in set-builder form.
4. What is the cardinality of each of these sets?
a) {{a}}
b) {a, {a}}
c) {a, {a}, {a, {a}}}
d) {∅}
e) {∅, {∅}, {∅, {∅}}}
5. Suppose that A is the set of sophomores at your school and B is the set of students in
discrete mathematics at your school. Express the following set in terms of A and B:
"the set of students at your school who either are not sophomores or are not taking discrete
mathematics"
a. A
c ∩ Bc
b. A
c U B
c
c. B-A
d. A-B
6. Let A be the set of students who live within one mile of school and let B be the set of
students who walk to classes. Describe the set B-A.
a. The set of students who walk to classes but live more than 1 mile away from school.
b. The set of students who walk to classes but live within 1 mile away from school.
c. The set of students who walk to classes.
7. What is the power set of the set {1, a, b}?
8. Let S = {∅, ?,{?}}Determine whether each of these is an element of S, a subset of S, neither,
or both.
a) {?}
b) {{?}}
c) ∅
d) { {∅ }, ?}}
8. Determine whether each of these statements is true or false.
a) 0 ∈ ∅
b) ∅ ∈ {0}
c) {0} ⊂ ∅
d) ∅ ⊂ {0}
e) {0} ∈ {0}
f) {0} ⊂ {0}
g) {∅} ⊆ {∅}
9. Let A = {a, b, c}, B = {x, y}, and C = {0, 1}.
Find A × B × C.
10. Find A2
if A = {0, a, 3}.

Conch Republic Electronics, Part 1

Conch Republic Electronics is a midsized electronics manufacturer located in Key West, Florida. The company president is Shelley Couts, who inherited the company. When it was founded over 70 years ago, the company originally repaired radios and other household appliances. Over the years, the company expanded into manufacturing and is now a reputable manufacturer of various electronic items. Jay McCanless, a recent MBA graduate, has been hired by the company’s finance department.

One of the major revenue-producing items manufactured by Conch Republic is a smartphone. Conch Republic currently has one smartphone model on the market, and sales have been excellent. The smartphone is a unique item in that it comes in a variety of tropical colors and is preprogrammed to play Jimmy Buffett music. However, as with any electronic item, technology changes rapidly, and the current smartphone has limited features in comparison with newer models. Conch Republic spent $750,000 to develop a prototype for a new smartphone that has all the features of the existing smartphone but adds new features such as WiFi tethering. The company has spent a further $200,000 for a marketing study to determine the expected sales figures for the new smartphone.

Conch Republic can manufacture the new smartphones for $220 each in variable costs. Fixed costs for the operation are estimated to run $6.4 million per year. The estimated sales volume is 155,000, 165,000, 125,000, 95,000, and 75,000 per year for the next five years, respectively. The unit price of the new smartphone will be $535. The necessary equipment can be purchased for $43.5 million and will be depreciated on a seven-year MACRS schedule. It is believed the value of the equipment in five years will be $6.5 million.

As previously stated, Conch Republic currently manufactures a smartphone. Production of the existing model is expected to be terminated in two years. If Conch Republic does not introduce the new smartphone, sales will be 95,000 units and 65,000 units for the next two years, respectively. The price of the existing smartphone is $385 per unit, with variable costs of $145 each and fixed costs of $4.3 million per year. If Conch Republic does introduce the new smartphone, sales of the existing smartphone will fall by 30,000 units per year, and the price of the existing units will have to be lowered to $215 each. Net working capital for the smartphones will be 20 percent of sales and will occur with the timing of the cash flows for the year; for example, there is no initial outlay for NWC, but changes in NWC will first occur in Year 1 with the first year’s sales. Conch Republic has a 21 percent corporate tax rate and a required return of 12 percent.

Conch Republic Electronics is a midsized electronics manufacturer located in Key West, Florida. The company president is Shelley Couts, who inherited the company. When it was founded over 70 years ago, the company originally repaired radios and other households appliances. Over the years, the company expanded into manufacturing and is now a reputable manufacturer of various electronic items. Jay McCanless, a recent MBA graduate, has been hired by the company's finance department. One of the Major revenue-producing items manufactured by Conch Republic is a smartphone. Conch Republic currently has one smartphone model on the market, and sakes have been excellent. The smartphone is a unique item in that it comes in a variety of tropical colors and is preprogrammed to play Jimmy Buffett music. however, as with any electronic item, technology changes rapidly, and the current smartphone has limited features in comparison with newer models. Conch Republic spent $750,000 to develop a prototype for a new smartphone that has all features of the existing smartphone but adds new features such as WiFi tethering. the company has spent a further $200,000 for a marketing study to determine the expected sales figures for the new smartphone.

Conch Republic can manufacture the new smartphone for $220 each in variable costs. Fixed costs for the operation are estimated to run $6.4 million per year. The estimated sales Volume is 155,000, 165,000, 125,000, 95,000, and 75,000 per year for the next five years, respectively. The unit price of the new smartphone will be $535. The necessary equipment can be purchased fro $43.5 million and will be depreciated on a seven-year MACRS schedule. It is believed the value of the equipment in five years will be $6.5 million.

As previously stated, Conch Republic currently manufactures a smartphone. Production of the existing model is expected to be terminated in two years. If Conch Republic does not introduce the new smartphone, sales will be 95,000 units and 65,000 units for the next two years, respectively. The price of existing smartphone is $385 per unit, with variable costs of $145 each and fixed costs of $4.3 million per year. If Conch Republic does introduce the new smartphone, sales of the existing smartphone will be 20 percent of sales and will occur with the timing of the cash flows for the year; for example, there is no initial outlay for NWC, but changes in NWC will first occur in Year 1 with the first year's sales. Conch Republic has 21 percent corporate tax rate and a required return of 12 percent.

Shelley has asked Jay to prepare a report that answers the following questions.

Questions:

1. What is the payback period of the project?

2. What is the profitability index of the project?

3. What is the IRR of the Project?

4. What is the NPV of the project?