Question 4 [20 marks] Analyze if the statements that are presented below are True or False. You MUST justify your answer to get credit. Answers without justification (even if they are correct) will be given zero marks.

(a) In any Pareto-optimal allocation of a two-good economy, each consumer has to consume a positive amount of both goods.

(b) A monopolist never produces on the elastic segment of its average revenue curve.

(c) If a firm’s production exhibits increasing returns to scale, then the firm’s marginal costs are decreasing and below its average costs.

(d) Maroon Theater practices third-degree price discrimination and sells tickets to three groups of customers: students, regular customers and senior citizens. The inverse demand of the three groups is linear. Furthermore, the students’ and senior citizens’ elasticities of demand for tickets are −4 and −3, respectively. Because the price charged to regular customers is greater than the price charged to senior citizens, we know with certainty that the ticket price for students will be lower than the ticket price for regular customers.

1. Functional foods are those containing nutritional supplements in addition to natural nutrients. Examples include orange juice with calcium and eggs with omega-3. Researchers examined college students’ attitudes toward functional foods. For American students, the results indicated that females had a more positive attitude toward functional foods and were more likely to purchase them compared to males. In a similar study, a researcher asked students to rate their general attitude toward functional foods on a 7-point scale (higher score is more positive). The results are as follows:

Females                     Males

n = 8                        n = 12

M = 4.69                  M = 4.43

SS = 1.60                  SS = 2.72

1. Do the data indicate a significant difference in attitude for males and females? Use α

= .05. Show all work, including clearly identifying hypothesis testing steps.

2. Compute the percent of variance accounted for by the gender difference to measure effect size.

Write a sentence demonstrating how the results of the hypothesis test and the measure of effect size would appear in a research report

Please I need help with this

Sam Suffolk is a student in MAT103 at SCCC. Sam has data from a random sample of 20 students that represents how many miles​ (rounded to the nearest whole​ mile) each student lives from the SCCC Ammerman campus. Sam organizes this data in the following frequency distribution table. Look at the table carefully and answer the questions that follow.

Sam made two mistakes when creating the classes for this table. Assuming​ Sam's frequencies are​ correct, despite the errors in the class​ limits, answer each of the following.

​Note: The first two lower class limits are correct.

​(a) Identify​ Sam's mistakes.

​(b) Can we determine how many students live 10 miles from the​ campus? If​ so, how​ many? If​ not, why​ not?

​(c) Give an estimate of the number of students in the sample that live more than 25 miles from the campus. If more than one frequency is​ possible, state all possible values.

1. Today’s local newspaper lists 27 stocks “of local interest.” Of these stocks, eleven increased, four decreased and twelve remained unchanged yesterday. If we decide to buy three of the stocks, what is the likelihood that all three increased yesterday?

2. You must select a committee of 6 from 28 students. How many different committees can be formed?

3. A survey of 538 students asked: What is your favorite winter sport? And, what type of college do you attend? The results are summarized below:

Using these 518 students as the sample, a student from this study is randomly selected.

1. What is the probability of selecting a student whose favorite sport is snowboarding and attends a four-year college?

2. If a graduate student is selected, what is the probability that the student prefers skiing?

3. The national mean score of an aptitude test is 50 with a standard deviation of 5. I think students at Ohio University can earn higher scores than people nationally. I survey 30 students at Ohio University and find a mean 57 with a standard deviation of 6.8. Is the mean scores of Ohio University students significantly more than the mean score of the aptitude test nationally? (use  = .05)

a. State the null and alternative hypotheses in symbols. (2 points)

b. Set up the criteria for making a decision. That is, find the critical value(s). (1 point)

c. Compute the appropriate test statistic. Show your work. (3 points)

d. Based on your answers above, evaluate the null hypothesis. (1 point) Reject Fail to reject (circle one)

e. State your conclusion in words. (1 point)

f. Given your decision, what type of error could have been committed? (1 point) Type I error Type II error (circle one)

A researcher is interested in finding a 90% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 128 students who averaged 42.3 minutes concentrating on their professor during the hour lecture. The standard deviation was 10.7 minutes. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a _____ (t? or z?) distribution.

b. With 90% confidence the population mean minutes of concentration is between ______ and ______ minutes.

c. If many groups of 128 randomly selected members are studied, then a different confidence interval would be produced from each group. About _____ percent of these confidence intervals will contain the true population mean minutes of concentration and about _____ percent will not contain the true population mean minutes of concentration.

g on their professor during a one hour statistics lecture. The study included 128 students who averaged 42.3 minutes concentrating on their professor during the hour lecture. The standard deviation was 10.7 minutes. Round answers to 3 decimal places where possible.

1. Two students are kayaking on the Saint John River. Initially, they are floating directly beside each other chatting and moving with the river current at 1.50 m/s downstream. Student A pushes away from Student B and sees Student B floating away from them at 1.00 m/s in the upstream direction. The combined inertia of Student A and their kayak is 100 kg and the combined inertia of Student B and their kayak is 120 kg. Assume that there is no friction between the kayaks and the water. a. Relative to the river flow, determine the velocities of the two students once they start moving away from each other (after the push). (Define your system to justify any conservation relations you might use, provide appropriate diagrams to describe the interaction and explain your solution approach.) b. What are the velocities of the two students once they are moving away from each other as seen from the perspective of someone on the shore of the river? c. What source energy does Student A expend in pushing the two kayaks apart?

The CUCG MPH Epidemiology students’ research team is planning to conduct a case-control study of the association between lack of adequate PPEs and covid19 infection among staff of Komfo Anokye Teaching Hospital in Kumasi. The students plan to study exposed nurses from the wards of the hospital as cases and unexposed nurses on retirement who live within the hospital flats as controls. As a reviewer of the research proposal;

a. Explain the type of bias which could arise from this study?

b. During the subject recruitment, most nurses on the ward for fear of covid19 stigmatization declined to enroll so the researchers recruited nursing administrators and other administrative staff who also work in the wards of the hospital. Explain the type of bias this particular decision could lead to.

c. Following your review, the students decided to change their research title to “Lack of adequate PPEs and covid19 infection within the Kumasi metropolis” and decided to use the nurses in Komfo Anokye Teaching Hospital as controls whilst recruiting the general Kumasi community for their subjects, discuss the type of bias they would be faced with.

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score ?μ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.810.8 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 510510 .

In answering the questions, use ?z‑scores rounded to two decimal places.

(a) If you choose one student at random, what is the probability that the student's score is between 505505 and 515515 ? Use Table A, or software to calculate your answer.

(Enter your answer rounded to four decimal places.)

(b) You sample 3636 students. What is the standard deviation of the sampling distribution of their average score ?¯x¯ ? (Enter your answer rounded to two decimal places.)

(c) What is the probability that the mean score of your sample is between 505505 and 515515 ? (Enter your answer rounded to four decimal places.)