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.)

In a school sports day, there are 110 students taking part in 3 events i.e. athletic, netball, and soccer. Some of them are also supporters. Overall 43 of them are girls. 40 students take part in athletic. There are 25 girls taking part in netball, and 5 play netball and athletic. As for boys, only 30 boys play soccer, and only 15 take part in athletic. Meanwhile, 20 students act as supporters. The number of boys who play soccer only is 6 times more than girls who take part in netball and athletic. Note that the events only girls play netball and only boys play soccer are mutually exclusive.

a. Illustrate the events. Write the proper symbol for each event.

b. If one student is selected, find the probability of:

i. student who play soccer and an athletic. (1 mark)

ii. student who play netball but not an athletic.
(1 mark)

iii. student who only take part in athletic.  

iv. student who take part in netball given that she is not an athletic, or the student play soccer.     

A Year 13 Statistics student was given an assignment where she had to design and conduct an experiment and analyse the data collected.

She decided to investigate whether being told that a quiz was easy or hard influenced the results of the quiz. All the students in a Year 9 class were given the same quiz after having been randomly allocated to one of three groups: Group 1 were told that it was a hard quiz, Group 2 were told it was an easy quiz and Group 3 were told nothing about the quiz. None of the students were told what the experiment was about.

She then carried out a randomisation test to compare the mean quiz marks for the three groups.

Which one of the following statements is false?

The response is the quiz mark.

There were 3 treatments; being told the quiz was easy, told it was hard or told nothing at all.

It was not possible to blind the students because they knew that they had been given a quiz.

The experiment used a completely randomised design.

The group that were told nothing about the quiz could act as the Control group.

Are teacher evaluations independent of grades? After the midterm, a random sample of 284 students were asked to evaluate teacher performance. The students were also asked to supply their midterm grade in the course being evaluated. In this study, only students with a passing grade were included in the summary table. Use a 5% level of significance to test the claim that teacher evaluations are independent of midterm grades.

Midterm Grade

(A) State the null and alternate hypotheses.

(B) Identify the appropriate sampling distribution: Chi-square test of independence, Chi-square goodness of fit, or Chi-square for testing or estimating σ² or σ.

(C) What is the value of the sample test statistic?

(D) Find or estimate the P-value.

(E) Based on your answers for parts (a) through (d), will you reject or fail to reject the null hypothesis?

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score μμ 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 500500 .

In answering the questions, use zz‑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 495495 and 505505 ? Use Table A, or software to calculate your answer.

(Enter your answer rounded to four decimal places.)

probability:

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

standard deviation:

(c) What is the probability that the mean score of your sample is between 495495 and 505505 ? (Enter your answer rounded to four decimal places.)

probability: