applications of statistical methods assignment.

É C O L E D E G E S T I O N T E L F E R S C H O O L O F M A N A G E M E N T

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ADM 2304 – ASSIGNMENT 2 Due date: Sunday, February 28 2021 at 11:30 pm (Brightspace). Instructions: • For each numerical question, you must first show your manual computations and then

use Minitab, MS Excel or any other statistical software to confirm your results. You must 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 will 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 files Assign2Data.mpx and Assign2Data.xlsx.

• Your assignment must be typed and uploaded to Brightspace in one single pdf file. You may upload several files, but only the most recent submission prior to the deadline will be graded. You must start each question on a different page and answer the questions in order. Students who fail to follow these instructions will be penalized with 10% of the marks (for example, if the assignment is marked out of 50, the penalty will be 5 marks).

• Late submissions will be accepted according to the late submission policy discussed in class and posted on Brightspace.

• Remember to include your integrity statement. Assignments submitted without a signed integrity statement will not be graded.

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Question 1 – House Prices in Halifax Larger homes generally fetch a higher price than smaller homes. The dataset Halifax includes information about a random sample of houses in Halifax. The sample includes 61 houses with one or two bedrooms and 37 houses with more than two bedrooms. The variable Large (1=Yes; 0=No) indicates whether the house has more than two bedrooms. The dataset also contains the Price ($) and Living Area (sq. ft.) for each listing. We are interested in the price difference between larger and smaller homes.

a) Describe, in one short phrase each, the populations being examined.

b) Carry out a parametric hypothesis test to see whether there is a real difference in the mean price of these two populations. Assume the two population variances are unequal and use a 5% significance level.

c) Find the corresponding 95% confidence interval for the difference in mean house prices. d) 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.

Question 2 – Consumer Spending Patterns You are on a financial planning team in charge of monitoring a high-spending segment of a credit card. You know that customers tend to spend more during December before the holidays, but you are not sure about the pattern of spending in the months after the holidays. The dataset Consumer_Spending has the monthly credit card spending of 400 customers during the months December, January, February and March, and the average across January to March.

a) Carry out a hypothesis test to compare December’s spending with the average spending over the three following months (variable JantoMarAvg) to confirm the belief that customers spend more on average in December. Use a 5% level of significance.

b) Construct the corresponding one-sided 95% confidence interval to supplement the

hypothesis test you carried out in part a). c) Does the confidence interval from part b) confirm your conclusion from part a)? Explain. Question 3 – Employee Salaries The human resources manager of a large company wants to compare the salaries of male and female employees. To that end, the manager selected a random sample of 22 female and 17 male employees. The dataset Salaries contains information on the salaries (in dollars) of these employees. Is the average salary the same for women and men?

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a) Are the samples independent? What is the appropriate parametric test here? Draw the

histograms of salaries for male and female employees and comment on the justification of using/not using a parametric test here to address the question of interest.

b) Regardless of you answer to part a), use an appropriate non-parametric test to compare the average salary of women and men at 5% level of significance. Make sure you follow all the steps for hypothesis testing indicated in the Instructions section and show your computations.

Question 4 – Illegal Drug Use Does self-reported illegal drug use vary by social class? To find out, a researcher questioned a random sample of 80 provincial residents about their occupation, education, and income. She then used this information to categorize residents as members of the upper, middle, working, and lower classes. Using appropriate sampling techniques, she interviewed them to see if they were using illegal drugs. Her results are as follows:

Upper class (24 total) 14 have said “Yes” 10 have said “No”

Middle class (18 total) 9 have said “Yes”

9 have said “No”

Working class (19 total) 8 have said “Yes” 11 have said “No”

Lower class (19 total) 6 have said “Yes”

13 have said “No”

a) Put the data into a two-way table with the drug use in the rows and the social classes in the columns. The data in this table should be observed counts.

b) Create another table with the corresponding expected counts and having row totals, column totals, and grand total. Round each cell value to two decimal places.

c) Perform a chi-square test to assess the association (or independence) between drug use

and social class at 5% level of significance. Verify the assumptions required for the chi- square test of independence. Make sure you follow all the steps for hypothesis testing indicated in the Instructions section and show your computations.