# QMS210: Applied Statistics for Business

QMS210: Applied Statistics for Business

GROUP

SPRING 2020

DUE: JULY 18 11:59PM

MARKS: Total marks = 70 (or 14% of the final grade)

PENALTY: There will be a 7-mark penalty (or 10% of the mark) for every day

after JULY 18 (including weekends) that the is late.

Notes:

1. No handwritten reports will be considered for marking purposes.

2. Submit one copy of the per group, file and indicate your group

number and the names and student numbers of all the group members. Failure to

indicate your group number will result in a 0 grade. There will be penalties for the

inclusion of unnecessary.

3. Present your solution for Hypothesis testing according to the template shown in

class. All relevant outputs (and ONLY relevant outputs) must be included.

4. Upload your file together with your report online via D2L under Group

Discussion

5. Read this entire document.

TOYOTA CAMRY Used car 2013

The Toyota was collected from a used car website in 2013. Choose the relevant variables

and answer the questions. The will be provided to you BUT your group must edit it

according to the instructions to select the 500 appropriate cases to analyze. The includes:

NUM- The unique index number of each auto 1-1300

Year - The model year of the car 2010, 2011, … Note that these are all Toyota Camrys.

Model - 4D SEDAN SE vs 4D SEDAN LE

Engine - 4 cylinders vs 6 cylinders

Condition - Below, Average, Above ALSO Condition# 1=Below 2=Avg 3=Above

Color - Colour of each car ALSO COLOR # Black=3 Red=5 Silver=6 White=7

Price - Price of each car sold

Odometer - The odometer reading of each car (mileage in miles)

2

How the is graded

Your submission will be graded based upon the following factors: substance, ,

accuracy, grammar and clarity. A demonstration of effort is the driving force of this assignment.

Assignments will be compared to discern levels of effort and excellence.

As a minimum, your report must include the following:

1. Title : [1] title [2] submission date [3] group number and the rows of the set

used [4] names of each group member plus their student number, [5] course code (i.e.:

CQMS210) [6] Submitted to “Instructor’s name”

2. Your must be submitted online via D2L under Group Discussion.

3. The answer to each question will begin on a new . State the question (cut and paste).

4. Cut and paste all relevant outputs in the write-up section the bottom of your

answer to each question. Do not send the reader to appendices to find them.

5. A complete write up of your chosen hypothesis test must include your assumptions and

conclusions. You must use both approaches (critical value and p-value approaches) to

make your statistical decisions.

6. Using the incorrect set of assigned to your group will result in getting a zero mark

for the . If you use from another group, both your group and the other group

will receive a zero mark. The for each group is for their group’s use only.

Group Size

This can be done in groups with 2 to 5 members only. This must be a team effort. It is

your responsibility to find your group members online via D2L under Communication → Group

Discussion Board. Your instructor (or D2L) has already assigned you a group number.

3

THERE ARE 6 QUESTIONS in this .

IMPORTANT:

Each GROUP HAS ITS OWN unique Set. You have been assigned to a group with a

specific group number by your instructor (or D2L). You can find the subset of the given of

size “500” for your group from the table above . Select your set based on the item numbers

from the file of 1300 autos. Individual projects (teams of 1) are NOT permitted. Contact your

instructor if the remainder of your team decides not to submit a project.

Question 1 (10 marks)

a) Based on the provided, construct a percentage frequency bar for the variable

COLOR: where the variable COLOR of the used car is described as BLACK, RED, etc …

b) Based on your bar , what is the most common COLOR? Include the in your report.

Question 2 (10 marks)

a) Find the measures of central tendency (mean, median & mode) for the variable

"Price” (Price of each car sold) and discuss the shape of this distribution. Which measure is

the best to represent “price” : the mean or the median. (Hint: Use 10% rule). Discuss

your rationale for the choice.

b) Find the measures of variability (range, IQR, variance and standard deviation) for "Price

of each car sold". Which of the two variables, the "Price” (Price of each car sold) or

"ODOMETER” (the mileage or usage of the car) is relatively more variable the

? (Hint: use the CVs) Include the output as part of your report.

ASSIGNMENT

Group # NUM

1 1 - 500

2 51 - 550

3 101 - 600

4 151 - 650

5 201 - 700

6 251 - 750

7 301 - 800

8 351 - 850

9 401 - 900

10 451 - 950

11 501 - 1000

12 551 - 1050

4

Question 3(10 marks)

i) Use the variable "ODOMETER" from your to construct 90% and 95%

intervals for the estimate of population mean “mileage” of used Toyota Camrys in 2013.

Interpret your intervals.

ii) Did you make any assumptions when constructing your intervals? If yes, which

assumptions; if not, why?

Question 4(10 marks)

Consider the claim that the average price of a used Toyota Camry in the USA at the time the

was collected was equal to $13,500. Use the variable “Price” to test this claim. (Use the 10%

level of significance).

Question 5 (10 marks)

[i] Based on your , is the mileage of used Camrys in the USA with 4 cylinders significantly

MORE the mileage of used cars with 6 cylinders? Test the 3% level of significance.

Note that only performs a 2-sided test.

[ii] Provide possible reasons why you should expect to find a significant statistical difference

between the prices of these 2 groups.

Question 6 (20 marks) Note the mark difference.

[i] Based on your , is there a significant difference in prices of used Camrys among the

different colours? State all your hypotheses and conclusions clearly in the standard format.

[ii] What are your results and conclusions from the Levene test?

[iii] Conduct the Tukey test (at the 5% level of significance) and describe the conclusions you

derive from this test.

[iv] If one assumed that the cost of new cars were independent of colour, then what choice ought

one to have made a decade ago to have maximized the resale value of these cars, based on this

old ? What pair of colours had the most significant difference? What pairs are

significantly different?

[v] This is old and current trends may differ. Research current colour preferences and give

your team’s advice and reasons as to what colours Toyota one should buy and NOT buy if the

only objective is to maximize final resale value.

5

HINTS: avoid these pitfalls

• The most common and biggest error is to assign one question to each person and put all

parts together. The outcome is almost always of very poor quality and receives a very

low grade. Our exams & tests also assume that each of you is expert in all facets of this

. You must check each ’s work- and fully understand it. It is a TEAM effort.

• The 2nd most common error is to postpone the assignment so late that you do not have

time to complete it. That is a sure way to do badly in this course.

• The 3rd most common mistake is to fail to monitor your team members. You must learn

to manage teams and make sure that you have all of the and reports the same time.

• You misread the question

• You used the wrong test (e.g., Using a Z test instead of a t test)

• Your test was in the wrong direction (or H1 has > or < instead of ≠)

• The null hypothesis or the alternative hypothesis (or both) was wrong

• You came to a wrong conclusion

• You used the wrong (or Incorrect inputs)

• Hypothesis missing μ or p or has the wrong one

• Ha contains one of {= ,≤ or ≥} OR Ho contains one of {>,<,or ≠}

• You used Sample in your hypotheses

• Failed to check the requirements to use a test

• Misread p-values or comparison of p to α is wrong

• Reaching a conclusion, i.e., rejecting H0, when p > α

• There is no technical conclusion (or a wrong one)

• There is no managerial conclusion (or a bad one)

• This test is a one-sided test (not 2-sided)

• You must take ½ of the Sig value from for a 1-sided test

• You failed to state the problem and/or define the variables.

• A printout of your IS MISSING! It had to be included!

• Missing LEVENE TEST of homogeneity

• Forget to discuss or check for normality