Religious essay
ADM 2304X – ASSIGNMENT 2
Professor: Afshin Kamyabniya
Total Marks: 64
Due date: Friday, June 12, 2020 at 11:59 pm.
Instructions:
• You may use MS Excel or other software for any calculations. However, you must show
your manual calculations when asked. You may paste your output onto your assignment to
show your use of software; however, this output does not replace any of the steps outlined
below. This means that answers that are exclusively software output may receive only
partial marks.
• If you are performing a hypothesis test, make sure you state the hypotheses, the level of
significance, the rejection region, the test statistic (and/or p-value, if requested), your
decision (whether to reject or not to reject the null hypothesis), and a conclusion in
managerial terms that answers the question posed. These steps must be completed in
addition to any software output.
• The data for this homework assignment can be found in the file Assign2Data.xlsx.
• Your assignment must be typed and uploaded to Brightspace in one pdf file. You may
upload several files, but only the most recent submission prior to the deadline will be
graded.
• No late submissions will be accepted.
• Remember to include your integrity statement.
Question 1 – Canada Small Business Financing Program (3 parts, 15 marks)
One of the support programs of the Government of Canada for small businesses is Canada Small
Business Financing Program (CSBFP). Under the CSBFP, the Government of Canada shares the
risk of default with the lender by guaranteeing 85 percent of the lender’s net eligible losses. Under
this program, small businesses may obtain financing for the following assets: real property
(immovables), equipment, and leasehold improvements. A fourth-year finance student at Telfer is
interested in seeing whether this program contributes to the growth of small businesses. She
randomly selected 18 IT firms operating in Ottawa that received support from the CSBFP in 2015.
She interviewed these companies and recorded the number of employees in 2014 and 2018. These
numbers are provided in dataset CSBFP.
a) [8 Marks] Carry out a hypothesis test to determine whether there was any increase in the size
of the IT firms operating in Ottawa that received support from the CSBFP in 2015. Explain your
approach in choosing a test, state the corresponding conditions, and show by using an appropriate
graph if the conditions are met. Copy the graph and use a 5% significance level. You may use MS
Excel or other software for your calculations.
b) [6 Marks] Using a confidence level of 95%, was there an increase in the size of the IT firms
operating in Ottawa that received support from the CSBFP in 2015? Calculate the corresponding
confidence interval manually and state your conclusion. You may use MS Excel or other software
for your computations.
c) [1 Mark] Does the confidence interval from part b) confirm your conclusion from part a)?
Explain.
Question 2- MBA Graduate Salaries (3 parts, 15 marks)
Assign2.xlsx in dataset MBA_Salary contains the annual salaries, in thousands of dollars, earned
by individuals who graduated with MBAs in 2015 and 2016 from a certain business school in
Canada. We would like to determine whether the distribution of salaries for 2015 MBA graduates
is higher than for 2016 MBA graduates.
a) [5 Marks] Create a boxplot and compare the distribution of salaries for 2015 and 2016
graduates.
b) [8 Marks] Perform the appropriate non-parametric test at a 5% significance level to determine
whether the salary for 2015 graduates is higher than for 2016 graduates. State the hypotheses
clearly and show your manual calculation for all the relevant steps in the test.
c) [2 Marks] Use Excel to perform the appropriate non-parametric test in part (b). How does the
result from Excel compare with your conclusion in part (b).
Question 3 – Beer bitterness (5 parts, 19 marks)
The taste of beers and its bitterness depends on the combination of its ingredients, mainly malts,
hops, and yeast. The bitterness of beers is specified by the International Bitterness Unit (IBU)
which measures the parts per million of a specific acid (isomerized alpha acid) found in one liter
of beer. Lower IBU corresponds to less bitterness and higher IBU corresponds to more bitterness.
In the Beer Bitterness dataset, you can find the level of bitterness measured in milligrams of
isomerized alpha acid in 1 liter of beer for two samples from two types of beer (Midnight Ottawa
and Midnight Montreal).
a) [2 Marks] Examine the boxplot of the level of bitterness for the sample of Midnight Ottawa
and the boxplot of the level of bitterness for the sample of Midnight Montreal. Copy the boxplot
and comment on the population distribution of the level of bitterness for each case.
b) [7 Marks] The manager of the brewery believes that Midnight Ottawa and Midnight Montreal
differ in terms of bitterness. Carry out a hypothesis test to see whether there is a real difference in
the mean level of bitterness of these two types of beer. You may use MS Excel or other software
for your computations and copy the result. Assume the two population variances are unequal and
use a 1% significance level.
c) [2 Marks] Find the corresponding 99% confidence interval for the difference in level of
bitterness. Show your computations.
d) [1 Mark] Describe in one sentence how the hypothesis test in part b) and the confidence interval
in part c) reflect the relationship between confidence intervals and hypothesis tests as introduced
in class.
e) [7 Marks] The manager of the brewery thinks that assuming unequal population variances is
wrong. Repeat part b), now manually, assuming equal population variances. Show your manual
calculations and clearly state your conclusion. (Hint. You may use any statistics you need from
part b)).
Question 4 – Top 100 Novels [15 marks]
Years ago a meme went around Facebook and other parts of the internet about the BBC’s “Top
100 Books”, with the statement that most people have read only six of the books listed. Your friend
at Carleton suggests that Carleton students have read more of those books than either uOttawa
students or UofT students. Determined to prove that uOttawa students are well read, you collect
some data. Using appropriate sampling techniques, you poll uOttawa, Carleton, and UofT students
to see how many of these books they’ve read. Here are the results of your poll:
uOttawa students (148 total): 84 have read 0 to 9 books on the list
43 have read 10 to 19
21 have read 20 or more
Carleton students (137 total): 91 have read 0 to 9 books on the list
24 have read 10 to 19
22 have read 20 or more
UofT students (119 total): 70 have read 0 to 9 books on the list
35 have read 10 to 19
14 have read 20 or more
a) [4 marks] Put the data into a two-way table with the number of books categories in the rows
and the university categories in the columns. The data in this table should be observed counts.
Create another table showing the corresponding expected counts. Show no more than three decimal
places in the second table and make sure your two tables show the totals for the rows, columns,
and overall.
b) [8 marks] Perform a hypothesis test to check if the distributions for number of books read are
the same across the three universities at the 0.01 significance level. That is, test the independence
of the two categorical variables, number of books read and university attended.
c) [3 mark] Is the chi-squared approach appropriate here? Why or why not? Hint: Look at the
“expected” table.