Unit Assignment #2 Questions

• Due no later than 11:00 p.m. on Sunday of Unit 4
• Worth 3% of final grade
• Graded out of 100 marks

1. Suppose your instructor wants to randomly choose one of the students in the class to ask a question.

Suppose the probability that the instructor asks Sam, one of your classmates, is 0.05 and the probability that she/he asks John, another student in your class, is 0.07. What is the probability that the instructor asks one of these two students (assuming independence between these events)?

2. What is wrong with the following statements? Explain your answer.

a. The probability that a student misses a class is 0.04 and the probability that he attends the class is 0.9

b. P (A and B) = -0.2

c. P (complement of A) = 0.7 given that P(A) = 0.7

3. A company has 750 employees. 450 of the employees are females. Half the female

are less than thirty years old, and one-fourth of the male workers are less than thirty years

old. If one of the workers of the company is selected at random to receive a prize, what is the

probability that the person selected is less than thirty years old?

4. The following table shows profit for 150 companies in 4 different industries:

	Less than or equal to 50 million	More than 50 million	Total
Auto Industry	17	15	32
Steel Industry	35	30	65
Food Industry	28	5	33
Wood Industry	10	10	20
Total	90	60	150

Assume we randomly choose a company, calculate the following probabilities:

a. The company has a profit less than or equal to 50 million.

b. The company is from the Auto industry.

c. The company is from the auto industry and has profit more than 50 million.

d. The company is either from the auto company or has a profit more than 50 million.

e. The company is from the auto industry given it has profit more than 50 million.

f. The company has a profit less than 50 million given it is not from the auto industry.

5. An accountant of an international company is working on a profit-and-loss report for the current fiscal year. The accountant reports that the company incurred a loss in 4 months out of the 12 months in the fiscal year. Let X be the number of months the company is suffering a loss in the next fiscal year. Discuss the adequacy of the model that X follows a binomial distribution with n = 12 and p = 4/12.

6. On average, you receive 3 junk e-mails every 6 hours. Assume that the number of pieces of junk mail you receive each day follows the Poisson distribution.

a. What is the expected number of junk e-mails in one day?

b. What is the probability of receiving exactly two junk e-mails in a six-hours interval?

c. What is the probability of receiving less than two junk e-mails arrive in a six-hours interval?

d. What is the probability of receiving two or more junk email in a six-hours interval?

7. A recent survey found that 83% of Canadian were satisfied with their current jobs. Answer the following questions based on a random sample of 10 Canadian workers:

a. What is the probability that exactly six employees were satisfied with their current jobs?

b. What is the probability that exactly nine employees were satisfied with their current jobs?

c. What is the probability that either four or five employees were satisfied with their current jobs?

d. What are the mean and standard deviation for this distribution?

Unit Assignment #3 Instructions

• Due no later than 11:00 p.m. on Sunday of unit8
• Worth 3% of final grade
• Graded out of 100 marks

Note: For time management purposes, students are strongly advised to submit their assignments by the due date above. Late penalties, however, will not be applied until after 8:00 AM the following day.

Late Submission Policy

• This assignment is subject to the Late Submission penalty policy, namely 5% per day for three days.
• This page will close and will not allow further submissions after this Late Submission period has expired.
• In the event of an emergency preventing you from submitting within this time frame, special permission must be obtained from your instructor. Documentation substantiating emergency is required. In such a circumstance, if the extension is granted, the professor will reopen the submission function for you on an individual basis.
• Please do not email your submissions to your professor, either before or after the due date; all coursework should be submitted through the online course (Moodle).

Instructions

Students are to complete the exercises in Word (or some other compatible word processor) and submit.

Unit Assignment #3 Questions

• Due no later than 11:00 p.m. on Sunday of Unit8
• Worth 3% of final grade
• Graded out of 100 marks

1. In a recent utilization survey of an e-learning platform of a post-secondary institution, a random sample of 64 students is selected (out a of a population of 5000 students). Their weekly hours of using this platform to perform learning activities are collected. After analyzing the data, a researcher states that he is 95% confident that the mean hours of the 5000 students is between 36.2 and 40.8 hours.

a. Explain the meaning of the statement reported by the researcher.

b. Suppose the population mean hours is later found to be 35.4 hours. The confidence interval reported by the researcher failed to cover the population mean. Discuss if there is anything wrong with the interval?

2. The property manager of a shopping mall claims that the mean score of their customer service is at least 85. Twenty-five customers were randomly selected to evaluate the customer service of the mall. The analysis via a hypothesis test shows that the P-value is less than 0.002 (i.e. p < 0.002).

a. State the null and alternative hypotheses.

b. Which distribution, normal or Student's t-distribution, is more appropriate for the hypothesis test? Why?

c. Explain the results of the hypothesis test in a way that could be understood by someone who has not studied statistics.

3. One study shows 60% of CEOs in the U.S hold a master's degree or doctorate. A random sample of 400 CEOs are selected in U.S. What is the probability that less than 55% of them have a master's degree or doctorate?

4. A statistician argues when sample size is big enough, the probability that the mean of the sample be higher than the mean of the population is the same as the probability that the mean of the sample be lower than the mean of population. Do you agree or disagree? Discuss your answer.

5. A simple random sample of 25 movies is taken from a movie website and the average lengths of them are found to be 150 min. The population standard deviation is known to be 10 min.

a. Test the hypothesis that the population mean length is greater than 145 min using the 0.05 level of significance.

b. Test the hypothesis that the population mean of movies length is different from 155 min using the critical value approach and a 0.05 level of significance.

6. The Ministry of health in BC wants to compare the average amount of time people spend in the Stanly Park versus English Bay during peak times to implement effective safety measures for COVID-19. A random sample of 25 persons in the Stanly Park spent an average of 14.6 minutes with a sample standard deviation of 5.8 minutes. A random sample of 27 persons in the English Bay spent an average of 11.5 minutes with a sample standard deviation of 4.9 minutes.

Perform a hypothesis test using = 0.05 to determine if the average time people spend in the Stanly park is more than the average time people spend in the English Bay.

7. In a completely randomized design, 7 experimental units were used for each of the three levels of the factor.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Treatment
Error	432076.5
Total	675643.3

a. Complete the ANOVA table.

b. Find the critical value at the 0.05 level of significance from the F-table for testing whether the population means for the three levels of the factors are different.

c. Use the critical value approach and = 0.05 to test whether the population means for the three levels of the factors are the same.

UNIT Assignment #4 Instructions

• Due no later than 11:00 p.m. on Sunday of unit10
• Worth 3% of final grade
• Graded out of 100 marks

Note: For time management purposes, students are strongly advised to submit their assignments by the due date above. Late penalties, however, will not be applied until after 8:00 AM the following day.

Late Submission Policy

• This assignment is subject to the Late Submission penalty policy, namely 5% per day for three days.
• This page will close and will not allow further submissions after this Late Submission period has expired.
• In the event of an emergency preventing you from submitting within this time frame, special permission must be obtained from your instructor. Documentation substantiating emergency is required. In such a circumstance, if the extension is granted, the professor will reopen the submission function for you on an individual basis.
• Please do not email your submissions to your professor, either before or after the due date; all coursework should be submitted through the online course (Moodle).

Instructions

Students are to complete the exercises in Word (or some other compatible word processor) and submit.

UNiT Assignment #4 Questions

• Due no later than 11:00 p.m. on Sunday of Unit10
• Worth 3% of final grade
• Graded out of 100 marks

1. A researcher believes that the engagement level of native students in PhD programs of Canada is less than international students. To test this hypothesis data was collected from a group of international students and native students. Data is represented in the following table:

Engagement Group of Students	High	Low	Total
International students	200	100	300
Native students	250	150	400

Test the hypothesis in 99% confidence level.

2. A researcher believes that 60% of managers in Canada have Visionary Management Style. To test this hypothesis, she collects a random sample of 200 mangers and realizes half of them follow Visionary Management Style. Test the hypothesis with 5% level of significance.

3. A researcher wishes to investigate the relationship amongst the distance between a house and the closest fire station in kilometers X (independent variable) and the damage that fire caused to them in thousand dollars as a dependent variable Y. A sample of houses from different parts of the city is randomly selected and the results are summarized in the ANOVA table below:

	Degrees of Freedom	SS
Regression	1	841.77
Residual	13	69.75
Total	14	911.52
	Coefficients	Standard Error	t Stat	p-value
Intercept	10.28	1.42	7.24	0.006
X variable	4.92	0.39	12.53	0.001

a. What is the estimated regression equation that relates the fire damage (Y) to the distance from the fire station (X)?

b. If a property is 5.8 kilometers away from the closest fire station what is the estimated damage in thousands of dollars?

c. Is the regression relationship significant? Use the p-value approach and 1% level of significance.

d. Compute the coefficient of determination between distance and the fire damage. Interpret the result in the context of the problem.

4. Assume you are working in a data analysis team at a company and you have access to volume of sales data over time. Last month, your company increased its YouTube ads, and the manager of the company thinks that these ads were very successful. One of your team members suggested a regression analysis to see if because of the increased ads, the volume of sales increased last month. What do you think about this suggestion? Assume that you decide to perform the regression analysis, what are the independent and dependent variables in your regression? If you run the regression and you find out that the slope coefficient of the regression is positive, does this necessarily mean your manager was right about the effect of new ads?