Michael is the owner of several successful bars and restaurants in central Melbourne. Recently, Michael was invited to make a guest appearance on a new hit television show about small business success stories. For his efforts, Michael received a one-off payment of $15,000. Michael feels he should be allowed to exclude this payment from his usual business income.

Required

Do you agree with Michael’s conclusion?

Students must give reasons for their answer. This discussion must include an analysis of the pertinent sections of the relevant legislation, rulings, and the relevant case law. If relevant, students must show calculations.

NOTE: It references to Australian Taxation law, please provide the reasons with their supportive sections number as well.

Monthly rent paid by undergraduates and graduate students.

(a) Construct a 90 percent confidence interval for the difference of mean monthly rent paid by undergraduates and graduate students, using the assumption of unequal variances with Welch's formula for d.f. (Do not round the intermediate calculations. Round your final answers to 3 decimal places. Negative values should be indicated by a minus sign.)
  
The 90% confidence interval is from which number to which number?

3.28. Adam is studying the relationship between hours of sleep and students GPA's. He passes a survey amongst his 17 students and the data he gathered is as follows

A.) Find the frequency distribution(S)

B.) Descriptive statistics (mean, medium, mode, range and standard deviation)

C.) Choose between t-Test and Z-Test

The following table shows the number of fifth and sixth grade teachers in a school district and the number of students in each of those grades. The number of teachers for each of the grade levels was determined by using the Huntington-Hill apportionment method. The district has decided to hire a new teacher for either the fifth or sixth grade.

(a) Use the apportionment principle to determine to which grade the new teacher should be assigned.  

(b) Use the Huntington-Hill apportionment principle to determine to which grade the new teacher should be assigned.

How does this result compare with the result in part (a)?

same result or different result

Decisions about alpha level may be different, especially as it relates from hard sciences to social sciences. For example, a medical trial for cancer treatments conducts their statistical tests at .0001 – so for every 1 out of 10,000 patients, there may be issues, sickness or even death. For social science, we use alpha .05. We are comfortable with performing research, for example, on students. So we are satisfied with losing 5 out of 100 students or having our results being incorrect 5 out of 100 times. Do you agree with these alpha levels? Why or why not? What if your child’s education and the teacher assigned to him/her would be successful 95 out of 100 times?

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 79 minutes and a standard deviation of 8 minutes. Answer the following questions. Round the intermediate calculations for z value to 2 decimal places.

1. What is the probability of completing the exam in one hour or less (to 4 decimals)?
   
2. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (to 4 decimals)?
   
3. Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time (to the next whole number)?

I need to understand how to do this in excel.

The amount of time to complete a physical activity in a PE class is approximately normally normally distributed with a mean of 37.5 seconds and a standard deviation of 7.6 seconds

a) What is the probability that a randomly chosen student completes the activity in less than 30.6 seconds? Round to 4 decimal places.

b)What is the probability that a randomly chosen student completes the activity in more than 42.9 seconds? Round to 4 decimal places

c)What proportion of students take between 33.5 and 43.4 seconds to complete the activity? Round to 4 decimal places.

d) 90% of all students finish the activity in less than ____ seconds

Answer: 0.182

Answer: 0.2387

Answer: 0.4819

Answer: 47.2

Problem 3. Americans average 6.9 hours of sleep on weeknights, according to a report released in 2011 by the National Sleep Foundation. The Dean of Student Affairs at the College of the Canyons wondered if the average amount of sleep on weeknights is less for students at their college. She collected data from a survey of 90 randomly selected students at her college. Respondents averaged 6.4 hours of sleep a night with a standard deviation of 1.35 hours. Here is the Statcrunch calculator printout.

a. State the hypothesis using ?

H0:

Ha:

b.Verify that the conditions are met for using a t-distribution.

c.Calculate the standard error to verify the value provided by the Statcrunch output below.

d.Based on the calculated p-value, what is our conclusion?

The Scholastic Aptitude Test (SAT) contains three parts: critical reading, mathematics, and writing. Each part is scored on an -point scale. A sample of SAT scores for six students follows.

a. Using a .05 level of significance, do students perform differently on the three portions of the SAT?

Bob is worried that students’ scores on examinations differ significantly based on the paper colors of the examinations, on average. Bob conducts an Analysis of Variance in which he selects four examinations at random for each of four paper colors.

a. If the value for Sum of Squares Total equals 2,144 and the value for Mean Squares Within equals 135.5, what does the calculated value for the associated test statistic equal?

(a) 1.2743

(b) 0.7819

(c) 1.6238

(d) 15.8229

b. If the level of significance equals 0.05, can Bob conclude students’ scores on examinations differ significantly based on the paper colors of the examinations, on average?

(a) not w/out Turkey's HSD

(b) Not w/out Hypotheses

(c) yes

(d) no