Question
(a) Consider a random sample of the following data: 254, 261, 250, 258, 253, 257.
Calculate the unbiased estimator of the population variance.
(1 mark)

(b) Suppose the GPA of all students enrolled in a particular course can be modelled by a
certain distribution with a mean of 3.4 and variance 0.3. Compute the probability that the
mean GPA of a random sample of 40 students selected from this course will be:

(i) lower than 3.2

(ii) between 3.3 and 3.6

(c) Suppose you throw a die 600 times. Apply a suitable technique to compute the
approximate probability of obtaining between 90 and 110 fours.

8. (15 pts) A person’s Intelligence Quotient (IQ) is determined via a series of test questions. The IQ score itself is designed to be approximately normally distributed with a mean value of 100 and a standard deviation of 15. In a sample of 20 students with behavioral problems, a school administrator observes an average IQ of 102.7. The administrator believes that students with behavioral issues have a different cognition from their peers, and thus a different average IQ. State the appropriate hypotheses; conduct a hypothesis test using α = 0.05 utilizing the classical approach, confidence interval approach, or p-value approach; state the decision regarding the hypotheses; and make a conclusion.

A researcher hypothesizes college students will be more extroverted than the population mean for extroversion and collects n = 177 students. The researcher performs a one-tail z test with alpha set to 0.05 and finds a sample z score is 2.44, showing evidence for the researcher's predictions. What is the probability (as % or proportion) the researcher made a type 1 error?

b. A researcher hypothesizes that coffee drinkers and non coffee drinkers will have different incidences of clinical anxiety. The researcher finds that those who drink more coffee are more likely to be anxious. Is this research a one tail or two tail test?

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Fast Pizza hires college students who drive their own cars to deliver pizzas to customers. Fast Pizza is concerned that the company may be liable for damages caused by company employees while they are driving their cars on company business.

Part 1: Discuss the loss exposures to both Fast Pizza’s business operation and to the students who are driving their own cars to deliver pizzas.

Part 2: Identify a commercial auto liability coverage that Fast Pizza could purchase to address their exposures.

Part 3: Discuss how the coverage purchased in Part 2 could impact the student drivers.  Use a loss scenario to illustrate.

Determine whether the following should be classified as simple random, systematic, convenience, stratified, or cluster sampling.

   ?    SimpleRandom    Systematic    Convenience    Stratified    Cluster      1. Every student in two different 8:00 classes on Tech's campus is selected to complete a survey

   ?    SimpleRandom    Systematic    Convenience    Stratified    Cluster      2. 50 people from each parish in Louisiana are asked political questions

   ?    SimpleRandom    Systematic    Convenience    Stratified    Cluster      3. Students are assigned numbers and a random-number generator selects students to participate in a survey

   ?    SimpleRandom    Systematic    Convenience    Stratified    Cluster      4. A researcher goes to the library to collect some published data

how to interpret confidence intervals and how NOT to interpret them.

What are the assumptions to justify the use of hypothesis testing?

If the null hypothesis is rejected, what can we conclude? If we know that 60% of ASU students like the parking and 50% of the community as a whole likes the parking, and the difference between the sample and population are tested, with the null rejected, what do we conclude? Is the difference significant? Not significant? Are ASU students significantly more likely or less likely to like the parking? Are they equally likely?

In order to reject the null when using a t distribution with small samples, what is needed? Consider size of the test statistic. Why?

It has been postulated that a student is more likely to smoke marijuana if both parents use alcohol and drugs. A paper published in Youth and Society (1979) reported that among 570 students whose parents use alcohol and drugs, 320 regularly smoke marijuana.

a. Is there any evidence that a student is more likely to smoke marijuana if both parents use alcohol and drugs?

b. Joann is planning for a new study on this problem. Suppose no prior information is available, what is the minimum sample size required such that the length of the 92.32% confidence interval for the true proportion of students smoke marijuana if both parents use alcohol and drugs is at most 0.075?

"Imagine that you are the director of student affairs at a small liberal arts college in the Midwest. During a staff meeting, the president of the college shares a number of complaints. The complaints allege that many LGBT students encounter prejudice and discrimination both on campus and among townspeople. The students feel that these problems are college-wide and need to be addressed by the president and her staff as well as by community leaders.

The president asks you to create an action plan. She feels that the college needs to open the lines of communication and encourage inclusive, honest dialogue on this issue.

Develop a summary of what you propose. Include the rationale behind your action plan."

An educational researcher wishes to know if there is a difference in academic performance for college freshmen that live on campus and those that commute. Data was collected from 267 students. Can we conclude that freshman housing location and academic performance are related? Location Average Below Average Above Average Total On campus 89 29 27 145 Off campus 36 43 43 122 Total 125 72 70 267 Copy Data Step 2 of 8 : Find the expected value for the number of students that live on campus and have academic performance that is average. Round your answer to one decimal place.

• Explain the services and products that are provided for all people in our country "free" at the point of sale ( IN THE USA)

1. Please list and discuss nine services and products that are provided to all people in our country "free" at the point of sale, (with the costs paid for by taxation).

2. Which one service or product on your list is the most important, in your opinion? Why?

3. Which one service or product on your list is the least important, in your opinion? Why?

4. If you had to add one more service or product on to the list, what would you add? Why? Why did you choose this service or product over all others? IN THE USA.