Suppose school has figured out a way to deliver the lectures all around the world in a way that creates a demand for their lectures because in some way they're better than the lectures that you could get from other universities. They evaluate the demand in Korea and demand in Germany. The demands are as follows: PK = 5,000 – 0.5QK PG = 3,000 – 0.5QG where PK and PG are the prices per course (per student) in Korea and Germany, respectively, and QK and QG are the number of students in Korea and Germany willing to enroll at those prices, respectively. The cost of online delivery is C = 1,800Q, where Q is the total number of students enrolled (i.e., Q = QK + QG). If school has decided to charge the same (uniform) tuition (price) to their online students everywhere around the world,

1. What price would they charge?

2. What would be their total online enrollment?

3. What would be their enrollment in Germany?

4. What would be their enrollment in Korea?

5. What would be the combined surplus in all the markets? I.e., what is the sum of the consumer surplus in Korea, consumer surplus in Germany, and school’s producer surplus from selling the instruction in both countries?

a.) A sociology professor has created a new assessment of political awareness. In using the assessment, she has determined that political awareness is normally distributed in college students with a population mean of 35.3 and a population standard deviation of 8.6.

Using the z-score found for the question above, what proportion of the population falls below a score of 22 on this test? Round your answer to four decimal places.

b.) A sociology professor has created a new assessment of political awareness. In using the assessment, she has determined that political awareness is normally distributed in college students with a population mean of 35.3 and a population standard deviation of 8.6.

What is the z-score for a student who gets a 43 on this test?

c.) A sociology professor has created a new assessment of political awareness. In using the assessment, she has determined that political awareness is normally distributed in college students with a population mean of 35.3 and a population standard deviation of 8.6.

Using the z-score found for the question above, what proportion of the population falls below a score of 43 on this test?

d.) What proportion of the normal distribution is below a z-score of -1.69. Round your answer to four decimal places.

Prof. Gersch knows that the amount of learning at YU is normally distributed with unknown mean and standard deviation of 2 hours. He surveys a random sample of 16 students and find that the average amount of learning that these students do per week is 19 hours. a) Construct a 95% CI for the true (pop) mean amount of learning. b) How many students should Prof. Gersch have surveyed so that the maximum margin of error in his 95% CI was 2 hours? c) Had someone told Prof. Gersch, prior to his sampling, that the true mean amount of learning was 18 hours per week, yet he thought the mean amount was greater, state the appropriate hypotheses and conduct the appropriate test at alpha of 0.05 using the sample evidence obtained. Use all possible methods here! Do the test also at alpha pf 0.01. What method is easier, why? d) Had Prof. Gersch suspected instead that the true mean amount of time spent on studying was different than 18 hours, state the appropriate hypotheses and conduct the appropriate test at alpha of 0.05 using the sample evidence obtained. Use all the possible methods here!

1.

You are conducting a study of students doing work-study jobs on your campus. Among the questions on the survey on the instrument are:

A. How many hours are you scheduled to work each week? Answer to the nearest hour.

B. How applicable is this work experience to your future employment goals?

Respond using the following scale: 1 = not at all, 2 = somewhat, 3 =very

Be sure to label the question you are working on:

a. Suppose you take random samples from the following groups: freshman, sophomores, juniors, and seniors. What type of sampling technique was used?

b. Describe the individuals of the study.

c. What is the variable for question A? What type of variable is it (quantitative or qualitative)? What is the level of measurement?

d. What is the variable for question B? What type of variable is it (quantitative or qualitative)? What is the level of measurement?

e. Is the proportion of responses “3=very” to question B a statistic or a parameter?

f. Suppose only 40% of the students you selected for the sample respond. What is the nonresponse rate? Do you think the nonresponse rate might introduce bias into the study? Explain.

g. Would it be appropriate to generalize the results of your study to all work-study students in the nation? Explain.

1. A high-school administrator who is concerned about the amount of sleep the students in his district are getting selects a random sample of 14 seniors in his district and asks them how many hours of sleep they get on a typical school night. He then uses school records to determine the most recent grade-point average (GPA) for each student. His data and a computer regression output are given below. (remember to do ALL parts).

Sleep (hrs) 9 8.5 9 7 7.5 6 7 8 5.5 6 8.5 6.5 8 8

GPA 3.8 3.3 3.5 3.6 3.4 3.3 3.2 3.2 3.2 3.4 3.6 3.1 3.4 3.7

(a) Do these data provide convincing evidence of a linear relationship between the hours of sleep students typically get and their academic performance, as measured by their GPA? Carry out a significance test at the α = 0.05 level. (10 points)

(b) Construct and interpret at 95% confidence interval for the slope of the regression of GPA on hours of sleep for seniors in this school district. (5 points)

(c) Can we conclude from these data that students’ GPA will improve if they get more sleep? Explain. (

Randomly selected students were given five seconds to estimate the value of a product of numbers with the results shown below.
Estimates from students given 1×2×3×4×5×6×7×8:

10000, 2040, 750, 4000, 42200, 6000, 1500, 5000, 500, 5000

Estimates from students given 8×7×6×5×4×3×2×1:

100000, 10000, 52836, 1200, 450, 100000, 200, 2050, 1500, 400

Use a 0.05 significance level to test the following claims:

Claim: the two populations have equal variances.

The test statistic is  
The larger critical value is  
The conclusion is
A. There is sufficient evidence to reject of the claim that the two populations have equal variances. (So, we can assume the variances are unequal.)
B. There is not sufficient evidence to reject the claim that the two populations have equal variances. (So, we can assume the variances are equal.)

Claim: the two populations have the same mean.

The test statistic is  
The positive critical value is  
The negative critical value is  
The conclusion is
A. There is not sufficient evidence to reject the claim that the two populations have the same mean.
B. There is sufficient evidence to reject the claim that the two populations have the same mean.

A clothes factory wants to produce school uniforms for high school students. To get an idea on the sizes of the clothes the factory collected data on the height of 30 high school students. The data are measured in centimeters and recorded in the following table.

1. What type of data is this? Explain
2. If the manager of the factory wants to create a histogram, how many classes she should use? Explain
3. What is the width of each class? Explain.
4. Create a histogram.
5. What shape does this histogram have?
6. f. What information the manager of the factory would get from this histogram?
7. Create an Ogive.
8. From the Ogive, show the percentage of students who are 170 centimeters or below.

17.

Refer to the scenario to answer the following questions.
A government worker surveys a number of households and comes up with the following information: there were a total of 90 people in the households, 10 of the people were children under 16, 10 of the people were retired but still capable of working, 35 people had full-time jobs, 5 had part-time jobs, 5 were stay-at-home parents, 5 were full-time students over the age of 16, 5 were disabled people who could not work, 10 people had no job but were looking for jobs, and there were 5 people who wanted a job but were not looking for a job.

According to the information in the survey, the unemployment rate is

19.

Due to the rising cost of a college education, a greater percentage of students have part-time jobs in comparison to past years. All else the same, this decrease in the number of full-time students can be expected to ________ the labor force participation rate and ________ the unemployment rate.

Critical Thinking Use the data set which shows student grades and the number of homework assignments missed. You can use the pivot table feature in excel to make a crosstabulation or contingency table as a first step. Choose the best statement below.

Grades and homework data, click here https://drive.google.com/file/d/1nDzzuY-pXeRqisc9sKpuKfXOMHXkBeLv/view?usp=sharing

A. Passing the class appears to be strongly and negatively related to the number of missed homeworks. The probability of not passing the class is fairly low for students that turn in all homework assignments, moderate for students that miss one assignment and quite large for students that miss more than two assignments.

B. There appears to be only a weak relationship between the number of missed assignments and the grades.

C. Missing a homework assignment is a strong predictor of not getting an exceeds expectations grade (A or B). For student that miss one homework assignment the probability of getting an A or B is extremely small.

D. The conditional probability of missing at least one homework assignment given that a student got a C suggests that it is more likely than not that a student with a C missed at least one assignment and this is an indicator that missing a homework assignment or more increases a student's probability of getting a C.

Consider a multiple-choice examination with 50 questions. Each question has four possible answers. Assume that a student who has done the homework and attended lectures has a 75% probability of answering any question correctly. A student must answer 43 or more questions correctly to obtain a grade of A. What percentage of the students who have done their homework and attended lectures will obtain a grade of A on this multiple-choice examination? A student who answers 35 to 39 questions correctly will receive a grade of C. What percentage of students who have done their homework and attended lectures will obtain a grade of C on this multiple-choice examination? A student must answer 30 or more questions correctly to pass the examination. What percentage of the students who have done their homework and attended lectures will pass the examination? Assume that a student has not attended class and has not done the homework for the course. Furthermore, assume that the student will simply guess at the answer to each question. What is the probability that this student will answer 30 or more questions correctly and pass the examination?

Is there a way to see this problem worked in Excel using the STDEV.S function? Would this be a one-tailed test or a two tailed test?