Instructions:

ANSWER 2 3 and 4 ONLY

1. Your assignment should be uploaded to Brightspace in pdf format.

2. You may use Minitab 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 Minitab; however, this output does not replace any of the steps outlined

below. This means that answers that are exclusively computer output may receive only one

mark.

3. If you are performing a hypothesis test, make sure you state the hypotheses, the level of

significance, the rejection region, the test statistic (and p-value, if requested), your decision

(whether to reject or not to reject the null hypothesis), and a conclusion that answers the

question posed or interprets the decision taken. These steps must be completed in

addition to any computer output.

4. The data in Minitab format can be found in the Bankruptcy_Index.mtw,

EatWell_Scores.mtw and HR_Ratings.mtw files; same data are also provided in the

Excel format file Assign2.xlsx under one of the three tabs with the above mtw names.

5. Remember to include your integrity statement.

1. [10 marks]

In a recent national survey, 30 Canadian adults aged 18-24 reported having used cannabis for the

first time since its legalisation in 2018 compared to 68 among the 25-44-year-olds. Out of the 1500

survey respondents, 125 were 18-24-year-olds and 400 were in the 25-44 age group. The Public

Health Agency has been concerned that the first time use of cannabis among the younger cohort

is higher than that among the older cohort.

a) Formulate the appropriate statistical hypotheses to test if the proportion of first-time cannabis

users is higher among younger adults.

b) Perform the appropriate hypothesis test manually using the P-value approach and a 2%

significance level. Make sure you verify that the relevant assumptions and conditions are met

for the test.

c) Using the corresponding confidence level, calculate a one-sided confidence interval for the

difference in the proportions of first-time cannabis users among the two age groups.

d) Are the results from b) and c) above consistent and why?

e) Use Minitab or other appropriate software to perform the calculations in b) and c) and comment

on any differences.

2. [10 marks]

The Office of the Superintendent of Bankruptcy of Canada (OSBC) is developing a new index to

measure the vulnerability of firms in the new technology industry. The index is a ratio of current assets

to current liabilities adjusted for various factors specific to this industry. The OSBC wants to compare

the index among healthy and failed firms for validation purposes. They expect that failed firms should

have a lower index than the healthy ones. Based on a Canadian business registry, they draw a

random sample of 68 firms still in operations and another random sample of 33 firms which failed in

the last 3 years. Index data for the sampled firms based on their latest financial statements are

included in the Minitab file Bankruptcy_Index.mtw and in the Excel file Assign2.xlsx under the

Bankruptcy_Index tab.

.

a) Use Minitab or other appropriate software to produce boxplots of the index values for the two

groups of firms and comment on their distribution.

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b) Use an appropriate statistical test to determine, at the 1% significance level, whether the data

provide evidence of a higher average index for the healthy firms. Make sure you provide your

manual calculations using the critical value approach.

c) Calculate manually a 99% one-sided confidence interval for the difference in the average index of

healthy and failed firms and compare your results with b) above.

d) Use Minitab or other appropriate software to perform the calculations in b) and c) above and

comment on any differences.

3. [10 marks]

EatWell Inc., a large fast-food chain company of Canada, wants to test two versions of a new product

before launching its full production. They select a random sample of individuals among their regular

clients and ask them to participate in an experiment to rate the product according to an assessment

grid worth 20 points. The 15 individuals who accepted to participate had to come to a specific

company location on two occasions during a given week to test the two versions of the product. It was

a randomized experiment in which the version assigned to participants during their first visit was

selected at random and participants did not know which version they were rating. Scores data of each

participant are included in the Minitab file EatWell_Scores.mtw and in the Excel file Assign2.xlsx

under the EatWell_Scores tab.

a) Examine and comment on the distribution of the ratings for the two versions of the product and

decide which statistical test is the most appropriate for this type of data. Justify your selection

based on the assumptions and conditions required for the most appropriate test selected.

b) Regardless of your answer in a) above, perform a relevant parametric test using a 10%

significance level to determine if there is a difference between the two versions of the product.

Make sure you show your Minitab or other software output along with an interpretation of the

results (manual calculations are not required here).

c) Now, perform a Wilcoxon signed rank test to verify if there is a significant difference at the 10%

level between the two versions of the product based on these ratings. Show your manual

calculations including the T+ and T- statistics and conclude based on the critical value approach.

d) Use Minitab or other software to perform the test in c) above and comment on the computed Pvalue and your conclusion in c).

e) Compare your results from the parametric and non-parametric tests above and state what the

final conclusion regarding the two versions of the product should be.

4. [10 marks]

The HR department of a large company needs to assign a newly hired director to either their

marketing development or their marketing operations division. To help in their decision, they organize

two discussion groups with randomly selected employees from each division. During the talks, the

director lays out his marketing vision and employees ask questions relevant to their daily work. At the

end, each employee has to rate the director on a scale from 1 to 10 (1=very bad; 10=very good). The

HR department wants to know if the distribution of ratings of the marketing development employees is

different among the employees of the two divisions. Ratings data for the two groups of employees are

included in the Minitab file HR_Ratings.mtw and in the Excel file Assign2.xlsx under the HR_Ratings

tab.

a) Examine the distributions of the ratings (show histograms) by the two groups of employees and

explain why a non-parametric test is justified to perform the analysis.

b) Perform an appropriate non-parametric test using a 5% significance level to determine if the

distribution of ratings of the marketing development employees is different than that of the

marketing operations employees. Specify any assumptions and/or conditions you need to make

to apply the test and state your hypothesis clearly. Show your manual calculations.

c) Use Minitab to perform the test in b) above and compare your results.