The publisher of an online newspaper knows that there are two types of customers. ‘students’ and ‘non-students’. Although they cannot distinguish what type of buyer is actually making a purchase of a subscription, they know the demand curves for each type of buyer. These are given by the following:

Students: p = 80 - q
Non students: p = 100 - q
where is q is the number of articles that are purchased. Assume that the marginal cost of supplying articles equals zero.
a. What is the maximum willingness to pay for 80 articles for the students?
b. What is the maximum willingness to pay for 80 articles for non students?
c. Assuming that buyers purchase the subscription that gives them the maximum consumer surplus, and they only purchase one subscription, what will student buyers and non-student buyers do if faced with the following choices:
Basic: 80 articles at $32 per month.
Premium: 100 articles at $50 per month
d. Assuming that buyers purchase the subscription that gives them the maximum consumer surplus, and they only purchase one subscription, what will student buyers and non-student buyers do if faced with the following choices:
Basic: 80 articles at $32 per month.
Premium: 100 articles at $35 per month

e. What is the highest price that can be charged for the premium version so that the non- students purchase this rather than the basic subscription, given the price of the basic is $32.

f. What is this pricing behaviour called?

We are interested in studying the performance of college students on statistics exams. In any
given semester, there are hundreds of students taking statistics in the department of psychology,
mathematics, business, or other related departments that offer a course on statistics. We
randomly select 20 students from the roster of all students enrolled in statistics for the spring
semester and administer questionnaires throughout the semester, as well as collect their
assignment and exam grades. In our first analysis, we are interested in examining the grades
from all the students on Exam 1 in their course. All exams were out of 100 points. This data is
below:

90 75 67 56 89 88 34 67 95 81 76 69 72 73 79 83 42 53 78 80

1. Draw a frequency distribution of the data. What can you determine from this
distribution?
2. What is your dependent variable and what scale of measurement is this variable?
pt.
3. We collected data from 20 students. Would you consider these students to be a
sample or population? Explain your answer in 1-2 sentences.
4. Is it important to have a normal distribution here? Why or why not?
5. Is this data skewed? Explain your answer?
6. Calculate the mean, median, and mode for this data.
7. Calculate the variance and standard deviation for this data using the table below.
Show all of your work.

Q: 10 students are going on a trip on which they will live close together. Where they are going, there is a disease which spreads easily among people who live close together. There is a vaccination against the disease. The vaccination costs 3 for each student who gets it. The students decide, individually and simultaneously, whether or not to get a vaccine. There are two types of students: the pro-vaccine type and the anti-vaccine type. For a pro-vaccine type, if she gets vaccinated, she will not get the disease and the trip brings her value 10. For a anti-vaccine type, if she gets vaccinated, she will not get the disease and the trip brings her value 9. If a student does not get vaccinated then the trip brings her value m, where m is the number of students who get vaccinated. A student’s payoff is the value of the trip minus the vaccination cost. Among the 10 students, 5 of them are pro-vaccine and 5 are anti-vaccine.

(a) Is there a NE in which some anti-vaccine types get vaccinated and some pro-vaccine types do not get vaccinated? Explain your answer. (5%)

(b) Is there a NE in which 5 students get vaccinated? Explain your answer. (5%)

(c) Is there a NE in which 7 students get vaccinated? Explain your answer. (5%)

(d) Find all the NE in pure strategies. Explain your answer. (10 %)

{NE is Nash Equilibrium}

Part A

The table below lists customer/car hires data. Each customer may hire cars from various outlets throughout Singapore. A car is registered at a particular outlet and can be hired out to a customer on a given date.

Instructions:

1. The data in the table is susceptible to update anomalies. Provide examples of how insertion, deletion, and modification anomalies could occur on this table.
2. Describe and illustrate the process of normalization by converting Table 1 to Third Normal Form (3NF) relations. Identify the primary and foreign keys in your 3NF relations.

Part B

The following tables form part of a database held in a Relational Database Management System for a printing company that handles printing jobs for book publishers:

Publisher                        (pubID, pubName, street, city, postcode, telNo, creditCode)

              BookJob                          (jobID, pubID, jobDate, description, jobType)

              PurchaseOrder               (jobID, poID, poDate)

              POItem                            (jobID, poID, itemID, quantity)

              Item                                  (itemID, description, onHand, price)

Where:

Publisher                          contains publisher details and pubID is the key.

BookJob                            contains details of the printing jobs (books or part books) and jobID is the key.

PurchaseOrder                 A printing job requires the use of materials, such as paper and ink, which are assigned to a job via purchase orders. This table contains details of the purchase orders for each job and the key is jobID/poID. Each printing job may have several purchase orders assigned to it.

POItem                              Each purchase order (PO) may contain several PO items. This table contains details of the PO items and jobID/poID/itemID form the key.

Item                                   contains details of the materials which appear in POItem, and the key is itemID.

Instructions:

Formulate the following queries using SQL:

(i)                         List all publishers in alphabetical order of name.

(ii)                        List all printing jobs for the publisher ‘Gold Press’.

(iii)                      List the names and phone numbers of all publisher who have a rush job (jobType = ‘R’).

(iv)                       List the dates of all the purchase orders for the publisher ‘PressMan’.

(v)                        How many publisher fall into each credit code category?

(vi)                       List all job type’s with at least three printing jobs.

(vii)                     List the average price of all items.

(viii) List all items with a price below the average price of an item.

Do faculty and students have similar perceptions of what types of behavior are inappropriate in the classroom? This question was examined by the author of an article. Each individual in a random sample of 173 students in general education classes at a large public university was asked to judge various behaviors on a scale from 1 (totally inappropriate) to 5 (totally appropriate). Individuals in a random sample of 98 faculty members also rated the same behaviors.

The mean rating for three of the behaviors studied are shown here (the means are consistent with data provided by the author of the article). The sample standard deviations were not given, but for purposes of this exercise, assume that they are all equal to 1.0.

(a)

Is there sufficient evidence to conclude that the mean "appropriateness" score assigned to wearing a hat in class differs for students and faculty? (Use α = 0.05. Use a statistical computer package to calculate the P-value. Use μ_Students − μ_Faculty. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t=

df=

P-value=

State your conclusion.

We do not reject H₀. We do not have convincing evidence that the mean appropriateness score assigned to wearing a hat in class differs for students and faculty.

We reject H₀. We do not have convincing evidence that the mean appropriateness score assigned to wearing a hat in class differs for students and faculty.    

We reject H₀. We have convincing evidence that the mean appropriateness score assigned to wearing a hat in class differs for students and faculty.

We do not reject H₀. We have convincing evidence that the mean appropriateness score assigned to wearing a hat in class differs for students and faculty.

(b)

Is there sufficient evidence to conclude that the mean "appropriateness" score assigned to addressing an instructor by his or her first name is greater for students than for faculty? (Use α = 0.05. Use a statistical computer package to calculate the P-value. Use μ_Students − μ_Faculty. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t=

df=

P-value=

State your conclusion.

We do not reject H₀. We do not have convincing evidence that the mean appropriateness score assigned to addressing an instructor by their first name is greater for students than for faculty.

We reject H₀. We have convincing evidence that the mean appropriateness score assigned to addressing an instructor by their first name is greater for students than for faculty.   

We reject H₀. We do not have convincing evidence that the mean appropriateness score assigned to addressing an instructor by their first name is greater for students than for faculty.

We do not reject H₀. We have convincing evidence that the mean appropriateness score assigned to addressing an instructor by their first name is greater for students than for faculty.

(c)

Is there sufficient evidence to conclude that the mean "appropriateness" score assigned to talking on a cell phone differs for students and faculty? (Use α = 0.05. Use a statistical computer package to calculate the P-value. Use μ_Students − μ_Faculty. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t=

df=

P-value=

State your conclusion.

We do not reject H₀. We have convincing evidence that the mean appropriateness score assigned to talking on a cell phone in class differs for students and faculty.

We reject H₀. We have convincing evidence that the mean appropriateness score assigned to talking on a cell phone in class differs for students and faculty.    

We do not reject H₀. We do not have convincing evidence that the mean appropriateness score assigned to talking on a cell phone in class differs for students and faculty.

We reject H₀. We do not have convincing evidence that the mean appropriateness score assigned to talking on a cell phone in class differs for students and faculty.

(d)

Does the result of the test in part (c) imply that students and faculty consider it acceptable to talk on a cell phone during class?

Yes, the result implies that students and faculty consider it acceptable to talk on a cell phone during class.

No, the result does not imply that students and faculty consider it acceptable to talk on a cell phone during class. In fact, the sample mean ratings indicate that only faculty feel the behavior is appropriate.    

No, the result does not imply that students and faculty consider it acceptable to talk on a cell phone during class. However, the sample mean ratings indicate that both groups feel the behavior is appropriate.

No, the result does not imply that students and faculty consider it acceptable to talk on a cell phone during class. In fact, the sample mean ratings indicate that both groups feel the behavior is inappropriate.

No, the result does not imply that students and faculty consider it acceptable to talk on a cell phone during class. In fact, the sample mean ratings indicate that only students feel the behavior is appropriate.

For students who first enrolled in two year public instituitons in a recent semester, the proportion who earned a bachelor's degree within six years was 0.388. The president of a certain college believes that the proportion of students who enroll in her institution have a higher completion rate.

A.) Determine the null & alternative hypotheses.

B.) Explain what it would mean to make a Type I error.

C.) Explain what it would mean to make a Type II error.

A.) State the hypotheses.

H0: _______

H1: _______

(Type integers or decimals. Do not round.).

B.) Which of the following is a Type I error?

1.) The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.388, when, in fact, the proportion is greater than 0.388.

2.) The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.388, when, in fact, the proportion is 0.388.

3.) The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.388, when, in fact, the proportion is 0.388

4.) The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.388, when, in fact, the proportion is greater than 0.388

C.) Which of the following Type II error

1.) The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.388, when, in fact, the proportion is 0.388.

2.) The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.388, when, in fact, the proportion is 0.388.

3.) The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.388, when, in fact, the proportion is greater than 0.388.

4.) The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.388, when, in fact, the proportion is greater than 0.388

A student counsellor is concerned about students’ stress levels. S/he wants to understand whether students in different courses have similar stress levels.

The following table shows a random sample of students in different courses and their stress levels (n= 178178). Use the table to answer the questions which follow.

1. (1 mark) What proportion of the students in the study have normal stress level? (3dp) Answer

2. (1 mark) What proportion of the Science students have low stress level? (3dp) Answer

3. (1 mark) What proportion of the students have high stress levels were Arts students? (3dp) Answer

The student counsellor would like to answer the following research question: Do students in different courses experience different stress levels? S/he sets up the following null and alternative hypotheses to answer the research question.

?0:H0: There is no association between enrolled course and level of stress. ?1:H1: There is an association between enrolled course and level of stress.

4. (1 mark) What is the expected value for Arts students who have low stress levels? (3dp) Answer

5. The absolute value of the test statistic is equal to (type your answer with 3 dp) Answer

6. (1 mark) The degrees of freedom is equal to (type your answer as an integer) Answer

7. (1 mark) The p-value is smaller than 0.05 Answertruefalse

8. (1 mark) We decide that Answerp -p value is greater than 0.05, therefore we do not reject the null hypotesisp -p value is less than 0.05, therefore we reject the null hypotesis

9. (2 mark) Our conclusion is that Answer -There is no association between enrolled course and level of stress. -There is an association between enrolled course and level of stress.

10. We are 95% confident that proportion of students with normal stress level for Science is between Answer (lower limit) and Answer (upper limit). Type your answers with 3dp.

A student counsellor is concerned about students’ stress levels. S/he wants to understand whether students in different courses have similar stress levels.

The following table shows a random sample of students in different courses and their stress levels (n= 200200). Use the table to answer the questions which follow.

1. (1 mark) What proportion of the students in the study have normal stress level? (3dp)  Answer

2. (1 mark) What proportion of the Engineering students have low stress level? (3dp)  Answer

3. (1 mark) What proportion of the students have high stress levels were Social Science students? (3dp)  Answer

The student counsellor would like to answer the following research question: Do students in different courses experience different stress levels? S/he sets up the following null and alternative hypotheses to answer the research question.

?0:H0: There is no association between enrolled course and level of stress. ?1:H1: There is an association between enrolled course and level of stress.

4. (1 mark) What is the expected value for Social Science students who have low stress levels? (3dp)  Answer

5. The absolute value of the test statistic is equal to (type your answer with 3 dp)  Answer

6. (1 mark) The degrees of freedom is equal to (type your answer as an integer)  Answer

7. (1 mark) The p-value is smaller than 0.05 Answertruefalse

8. (1 mark) We decide that Answerp value is greater than 0.05, therefore we do not reject the null hypotesisp value is less than 0.05, therefore we reject the null hypotesis

9. (2 mark) Our conclusion is that AnswerThere is no association between enrolled course and level of stress.There is an association between enrolled course and level of stress.

10. We are 95% confident that proportion of students with normal stress level for Engineering is between  Answer (lower limit) and  Answer (upper limit). Type your answers with 3dp.

A student counsellor is concerned about students’ stress levels. S/he wants to understand whether students in different courses have similar stress levels.

The following table shows a random sample of students in different courses and their stress levels (n= 208208). Use the table to answer the questions which follow.

1. (1 mark) What proportion of the students in the study have normal stress level? (3dp) Answer

2. (1 mark) What proportion of the Arts students have low stress level? (3dp) Answer

3. (1 mark) What proportion of the students have high stress levels were Law students? (3dp) Answer

The student counsellor would like to answer the following research question: Do students in different courses experience different stress levels? S/he sets up the following null and alternative hypotheses to answer the research question.

H0:H0: There is no association between enrolled course and level of stress. H1:H1: There is an association between enrolled course and level of stress.

4. (1 mark) What is the expected value for Law students who have low stress levels? (3dp) Answer

5. The absolute value of the test statistic is equal to (type your answer with 3 dp) Answer

6. (1 mark) The degrees of freedom is equal to (type your answer as an integer) Answer

7. (1 mark) The p-value is smaller than 0.05 Answertruefalse

8. (1 mark) We decide that Answerp value is greater than 0.05, therefore we do not reject the null hypotesisp value is less than 0.05, therefore we reject the null hypotesis

9. (2 mark) Our conclusion is that AnswerThere is no association between enrolled course and level of stress.There is an association between enrolled course and level of stress.

10. We are 95% confident that proportion of students with normal stress level for Arts is between Answer (lower limit) and Answer (upper limit). Type your answers with 3dp.

A student counsellor is concerned about students’ stress levels. S/he wants to understand whether students in different courses have similar stress levels.

The following table shows a random sample of students in different courses and their stress levels (n= 214214). Use the table to answer the questions which follow.

1. (1 mark) What proportion of the students in the study have normal stress level? (3dp) Answer

2. (1 mark) What proportion of the Science students have low stress level? (3dp) Answer

3. (1 mark) What proportion of the students have high stress levels were Human Sciences students? (3dp) Answer

The student counsellor would like to answer the following research question: Do students in different courses experience different stress levels? S/he sets up the following null and alternative hypotheses to answer the research question.

H0:H0: There is no association between enrolled course and level of stress. H1:H1: There is an association between enrolled course and level of stress.

4. (1 mark) What is the expected value for Human Sciences students who have low stress levels? (3dp) Answer

5. The absolute value of the test statistic is equal to (type your answer with 3 dp) Answer

6. (1 mark) The degrees of freedom is equal to (type your answer as an integer) Answer

7. (1 mark) The p-value is smaller than 0.05 Answertruefalse

8. (1 mark) We decide that Answerp value is greater than 0.05, therefore we do not reject the null hypotesisp value is less than 0.05, therefore we reject the null hypotesis

9. (2 mark) Our conclusion is that AnswerThere is no association between enrolled course and level of stress.There is an association between enrolled course and level of stress.

10. We are 95% confident that proportion of students with normal stress level for Science is between Answer (lower limit) and Answer (upper limit). Type your answers with 3dp.