Discreet Math Question:

Suppose you have 100 students in school. Principal wants to take photos in different ways so that every student thinks they have been treated fairly.

1.She wants to divide 100 students into groups of 10 and take one photo of each group. So no student is in more than one photo and she doesn't care how they are lined up. How many photo are going to need to be taken in this situation?

2. She has a new idea that includes three of the schools teachers. She still wants to divide the 100 students into groups of 10. With each student, they will take a picture with every possible way to choose two of the three teachers, with one on the left and other on the right (So Order Matters). How many photos are going to be needed in this situation?

The reading speed of sixth-grade students is approximately normal with a mean speed of 125 words per minute and a standard deviation of 24 words per minute.
(Note: Labelled diagrams and proper notation are required for part a), b), c).)
a) What is the probability that a randomly selected student will read more than 130 words per minute? Interpret this probability.
b) What is the probability that the mean reading rate for a random sample of 12 sixth-grade students is more than 130 words per minute? Interpret this probability.
c) What is the probability that the mean reading rate for a random sample of 24 sixth-grade students is more than 130 words per minute? Interpret this probability.
d) Compare the probabilities in part b) and part c). What effect does increasing the sample size have on the probability?

1). A sample of 8 football teams in the Fresno Conference scored a mean of 20.8 points per game in the 2019 season, with a known population standard deviation of 3.2 points. A sample of 10 football teams in the Madera Conference scored a mean of 24.5 points per game in the 2019 season, with a known population standard deviation of 2.6 points. At the 0.01 significance level, can we conclude that the mean points scored in the Fresno Conference is less than the mean points scored in the Madera Conference?
2). A sample of 50 students at Bullyard High School found that 4 of them had green eyes. A sample of 40 students at Cowtown High School found that 5 of them had green eyes. At the 0.02 significance level, can we conclude that there is a difference in the proportion of students with green eyes between Bullyard and Cowtown High School.

Students will select one of the Options listed for each of the applications and will complete a draft essay for each of the applications. The drafts will be submitted for grading by the end of Week 6.

APPLICATION 3: Law of SUPPLY AND DEMAND:

Prior to completing the application, it is highly recommended that students review Chapter 3 to gain a solid foundation.

Option 1: LAW OF DEMAND AND CIGARETTES

Option 2: LAW OF SUPPLY AND WOOLYMPICS

APPLICATION 4: Market Analysis (Equilibrium)

Prior to completing the application, it is highly recommended that students review Chapters 3 and 4 to gain a solid foundation.

Option 1: Equilibrium: CHINESE DEMAND AND PECAN PRICES

Option 2: Equilibrium: HONEYBEES AND THE PRICE OF ICE CREAM

Option 3: WHY LOWER DRUG PRICES?

I need only one answer in EACH application! So please choose just one Thank You!!!

A survey was conducted at a college to determine the number of hours students spent outside on weekends during the winter. For students from cold weather climates, the results were M = 8, SD = 1.5. For students from warm-weather climates, the results were M = 5, SD = 4.2. Explain what these numbers mean to a person who has never had a course in statistics, and suggest conclusions the person can draw from these results. These conclusions use the means, raw scores, and variability in in your explanations.

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If playing video games and aggression are correlated, give two REASONS that explain why we cannot infer causality from this correlation? Describe how each limits causality. Explain a situation (explicitly) that is a slight exception to one of the reasons.  

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The MVSU Student Association (MVSUSA) is planning a fundraising event for the spring semester. The MVSUSA is planning to hire the B B King Band as entertaining for a fee of $750. The BB King Museum in Indianola was selected as the site for the event. The Museum will charge the MVSUSA $600 for the use of it's banquet room. Thompson's Hospitality was selected to cater the event. Thompson's Hospitality will charge the MVSUSA a flat fee of $400 and an additional charge of $20 per meal.

a) The MVSUSA expects a total of 250 students and alumni to attend its spring fundraising event. What is the break-even ticket price?

b) The MVSUSA is considering charging two different ticket prices: $25 for students and $75 for alumni. If the expected ratio of students to alumni is three to one, how many student tickets and how many alumni tickets must each be sold in order for the spring fundraising event to break-even?

The university wants to examine whether students spend enough time on their remote classes after switching to the online teaching. The university staff sends a survey to 50 random students and asks for the study time per week after the spring break. The mean study time per week of the sample is 25.5 hours. It is believed that the population standard deviation is 3.5 hours. The university wants to know whether the students have spent at least 23 hours per week on average in their remote study.

 What is the correct form of the statistical hypothesis?

 What is the value of the test statistics?

 If you decide to use the critical value approach to perform the test, what is the corresponding critical value for the test at 95% confidence level?

 If you decide to use the P-value approach to perform the test, what is your P-value?

 What is your conclusion at the 95% confidence level?

A small college has only 4 students and offers only 3 majors: Art, English, and Physics.

Suppose that the 4 students are assigned to these 3 majors at random with probabilities P[Art] = 1/4, P[English] = 1/2, P[Math] = 1/4.

Let A, E, and M denote the numbers of students assigned to Art, English, and Math, respectively

(i) What is the probability distribution of A? E? M? State the expected values and variances of each.

(ii) What is the joint probability distribution of (A, E, M)? State the joint probability mass function f(a, e, m) = P[A = a, E = e, M = m].

(iii) What are Cov(A, E), Cov(A, M), Cov(E, M)? Are A, E, and M independent?

(iv) Find the probability that each major has at least 1 student.

At Rochester Institute of Technology, 34% of the students are female. The Department of Mathematics and Statistics would like to know if the Data Analysis course has a different percentage of female students. From a random sample of 50 students taking this course, 23 were female. Does this data support that the proportion of females taking this class is different from the percentage of females in the school?

The appropriate hypotheses would be:

A) H o μ = 34 a n d H A μ ≠ 34

B) H o p = 0.34 a n d H A p ≠ 0.34

C) H o p ≤ 0.34 a n d H A p > 0.34

D) H o p ≥ 0.34 a n d H A p < 0.34

Answer: A, B, C, D?

The Test Statistic would be:?

The P-value would be:?   

The Conclusion would be:?

In our Eco 207 class, we have a policy that says we take the best three out of four of your exam grades and count then toward your overall course grade. In other words, we drop the lowest score. (below, assume that the professor’s goals are to have the students work hard all semester long, and obtain good grades)

a. What part of this policy provides a positive incentive to do well?

b. What is problematic about this policy from the perspective of students? Professors?

Now imagine an alternative policy. Instead of dropping the lowest exam grade, we drop the highest exam score.

c. What part of this policy provides a positive incentive to do well?

d. What is problematic about this policy from the perspective of students? Professors? (in your answers above, assume that the median exam grade for the course always corresponds to a B-).