The National Sleep Foundation (NSF) recommends that college students get between 8 and 9 hours of sleep per night. Not believing this is happening at a local college, a random sample of 20 students resulted in a mean of 6.94 hours, with a standard deviation of 1.1 hours.

Part 1 of 3

If it is assumed that hours of sleep for college students is approximately normally distributed, construct and interpret a 95% confidence interval statement as well as a confidence level statement. Do the students at this local college meet the NSF recommendation? (Round your answers to two decimal places. Use a table or technology.

The University of Pittsburgh Medical (UPMS) School grades each class in the following manner:

All students whose score is plus or minus two standard deviations from the mean course score receive a grade of “Pass.”

Students whose score is above two standard deviations from the course mean receive a grade of “Pass with Distinction.”

And, students whose score is below two standard deviations from the course mean receive a grade of “Fail.” Course scores are always assumed to be normally distributed.

Approximately what percentage of medical students in each class receives a “Pass with Distinction”?

Two students take the same test which consists of 5 questions, each one with 5 answers, each one with only 1 correct answer. If the students respond the test randomly

i) What is the probability that both of the students get the same number of correct answers?

ii) Find the probability that both tests are the same (assume that each test is independent from each other)

iii) What is the expected number of correct answers for each student?

iv) What is the probability that both students pass the test if they have to get at least 3 correct answers to pass it?

You’ve been assigned to set the price at the local movie theater. You know that market demand can be broken into two groups, students and non-students. Those functions are: Students: p = 12 − 1/4q Non-Students: p = 22 − q (if you aggregated those functions, you would obtain p = 22 − q if p > 12 and p = 14 −1/5q if p ≤ 12). You’ve also been given the total cost and marginal cost for the theater. TC = 6 + 2q + q^2, MC = 2 + 2q

a) Plot the inverse demand curves for students and non-students. Make sure to also include both marginal revenue curves and supply curves, as well as labeling correctly.

b) Now, let’s assume that you can only charge one price for tickets. What is the equilibrium price, quantity and profits if you choose to act as a monopolist?

c) You’ve decided to try price discrimination for each group. What is the equilibrium price and quantity for students and non-students? What is your new total profit? Round answers to two decimal places.

d) Do the prices in part (c) make sense? Why would the price for one group be higher than the price for the other group?

e) What kind of price discrimination is this? Is there any way you can prevent arbitrage in this case? If so, how? Why is it important to prevent arbitrage in price discrimination?

Coaching companies claim that their courses can raise the SAT scores of high school students. But students who retake the SAT without paying for coaching also usually raise their scores. A random sample of students who took the SAT twice found 427 who were coached and 2733 who were uncoached. Starting with their verbal scores on the first and second tries, we have these summary statistics: Try 1 Try 2 Gain n n x ¯ ¯ ¯ x¯ s s x ¯ ¯ ¯ x¯ s s x ¯ ¯ ¯ x¯ s s Coached 427 500 92 529 97 29 59 Uncoached 2733 506 101 527 101 21 52 Estimate a 96% confidence interval for the mean gain of all students who are coached. to at 96% confidence. Now test the hypothesis that the score gain for coached students is greater than the score gain for uncoached students. Let μ 1 μ1 be the score gain for all coached students. Let μ 2 μ2 be the score gain for uncoached students.

(a) Give the alternative hypothesis: μ 1 − μ 2 μ1−μ2 0 0 .

(b) Give the t t test statistic:

(c) Give the appropriate critical value for α= α= 5%: . The conclusion is A. There is sufficient evidence to support the claim that with coaching, the mean increase in scores is greater than without coaching. B. There is not sufficient evidence to support the claim that with coaching, the mean increase in scores is greater than without coaching.

please show your work . thank you !

#1. Impact Evaluation

   In the move to online instruction due to COVID-19, Development University was concerned that its students may not have the technology they needed at home to keep up with their classes. In order to address this issue, at the start of the term, the University offered all students coupons for a 50% price discount on a new iPad. The hope was that the iPad would allow students to participate more fully in their online classes, and therefore allow them to learn more.

    Development University heard that you have learned how to do impact evaluation in your economics classes, so asked you to evaluate how well the iPads worked for their students. In particular, they wanted to know if the iPads caused student grades to improve. In looking at the data, you notice that although all students were offered the coupon, only half of them purchased an iPad through the program. Therefore, you decide to compare the average GPAs of students who purchased an iPad to those who didn't. You find that students who purchased an iPad had an average GPA of 3.4, and students who did not purchase an iPad had an average GPA of 3.1.

1) Explain in words one sentence that clearly describes the context of this study. (The answer should clearly define the treatment and the outcome variable in this study, not just the abstract language of what y0i means in general.)

2) Please explain and describe ?[?1?|??=0] in the context of this study. (The answer should demonstrate a clear understanding of both the treatment and the outcome variable in this study.

Statistic

Q4 (a) On a sunny day, a theme park had 1,000 visitors. According to the attendance record, 800 visitors took a ride on the roller coaster; 450 visitors took a ride on the merry-go-round. It is estimated that among those visitors who took a ride on the roller coaster, 40% of them also took a ride on the merry-go-round. A visitor on that day is selected at random.

i. What is the probability that this visitor rode on both rides?

ii. What is the probability that this visitor rode on no rides at all?

iii. If this visitor has taken a ride on the merry-go-round, what is the probability that he has not ridden on the roller coaster?

Q4(b) In a tutorial session, there are 11 Japanese students, 6 American students and 8 Australian students. Among these 25 students, a group of 5 students is selected randomly for the first presentation.

i. How many different groups can be formed?

ii. What is the probability that this group consists of only Japanese students?

iii. What is the probability that this group consists of exactly 2 Japanese students and 3 American students?

Q4(c) Three urns contain colored balls. Urn 1 contains 3 red, 4 white and 1 blue balls. Urn 2 contains 4 red, 3 white and 2 blue balls. Urn 3 contains 1 red, 2 white and 3 blue balls. One urn is chosen at random and a ball is drawn from it. If the ball is red, what is the probability that it came from Urn 3?

Franklin Training Services (FTS) provides instruction on the use of computer software for the employees of its corporate clients. It offers courses in the clients’ offices on the clients’ equipment. The only major expense FTS incurs is instructor salaries; it pays instructors $5,300 per course taught. FTS recently agreed to offer a course of instruction to the employees of Novak Incorporated at a price of $490 per student. Novak estimated that 20 students would attend the course. Base your answers on the preceding information.

Required

1. Relative to the number of students in a single course, is the cost of instruction a fixed or a variable cost?

2. Determine the profit, assuming that 20 students attend the course.

3. Determine the profit, assuming a 10 percent increase in enrollment (i.e., enrollment increases to 22 students). What is the percentage change in profitability?

4. Determine the profit, assuming a 10 percent decrease in enrollment (i.e., enrollment decreases to 18 students). What is the percentage change in profitability?

The instructor has offered to teach the course for a percentage of tuition fees. Specifically, she wants $250 per person attending the class. Assume that the tuition fee remains at $490 per student.

6. Is the cost of instruction a fixed or a variable cost?

7. Determine the profit, assuming that 20 students take the course.

8. Determine the profit, assuming a 10 percent increase in enrollment (i.e., enrollment increases to 22 students). What is the percentage change in profitability?

9. Determine the profit, assuming a 10 percent decrease in enrollment (i.e., enrollment decreases to 18 students). What is the percentage change in profitability?

Case:

  In the move to online instruction due to COVID-19, Development University was concerned that its students may not have the technology they needed at home to keep up with their classes. In order to address this issue, at the start of the term, the University offered all students coupons for a 50% price discount on a new iPad. The hope was that the iPad would allow students to participate more fully in their online classes, and therefore allow them to learn more.

    Development University heard that you have learned how to do impact evaluation in your economics classes, so asked you to evaluate how well the iPads worked for their students. In particular, they wanted to know if the iPads caused student grades to improve. In looking at the

data, you notice that although all students were offered the coupon, only half of them purchased an iPad through the program. Therefore, you decide to compare the average GPAs of students who purchased an iPad to those who didn't. You find that students who purchased an iPad had an average GPA of 3.6, and students who did not purchase an iPad had an average GPA of 3.0.

Explain and describes the context of this study? (The answer should clearly define the treatment and the outcome variable in this study)

Please explain and describe E[y1i|D=0] in the context of this study?

Come out with a formula that represents your observed estimate of the average effect of the iPads on student grades. As described above, your estimate is the difference in grades between those who purchased an iPad and those who didn't.

1.Test the hypothesis that the proportion of students who have the Wuhan flu is .3. Use a .10 significance level, a two-tail test and the following data: A sample of 100 students has 40 with the virus.

2 Test the hypothesis that the mean number of hours the Wuhan flu can live on a cell phone is more than 20. Use a .01 significance level and a one tail test and the following data: a sample of 50 phones has a sample mean =21.5 and a variance=9.

3 Test the null hypothesis that the proportion of students who believe TRUMP policy is appropriate dealing with the TRUMP virus is .6. The alternative hypothesis is the proportion >.6. Use a .05 significance level. A sample of 25 students has 19 think TRUMP policy is effective.

4) Are students avoiding events that average more than 20 people? A sample of 25 event has an average attendance of 23.3 people and a variance of 4 people. Use a significance level of 5% and a one-tail test.

5. Is the vaccine effective for the Wuhan flu? A sample of 30 students were given the vaccine and 12 got the virus. Without the vaccine, the rate of infection is 50%. Use a 1 tail test and a 5% significance level. What is the p value. [Khan academy has a good discussion of the P value]

6. Do students spend more than 6 ours a day on the phones? A sample of 150 students has an average usage of 8 hours and a variance of 6 hours. Use a 10% significance level.