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ADM 2304 – ASSIGNMENT 1 (Weeks 1-2-3)

Due date: Sunday, February 5, 2023, at 11:59 pm (Brightspace).

Instructions:

• You may use StatCrunch, MS Excel Analysis ToolPak, 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. Include your output when asked to confirm results.

• If you are performing a hypothesis test, make sure you state the hypotheses, the level of significance, the decision criteria/region, the test statistic, and/or the critical value 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 assignment can be found in the file Assign1Data.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. Start each question on a different page and answer the questions in order.

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

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

• Students who fail to follow any of the instructions above will be penalized with 10% of the marks (for example, if the assignment is marked out of 50, the penalty will be 5 marks).

IMPORTANT ADVICE FOR CALCULATIONS

Always use at least 3 decimal places all along your intermediate calculations and apply proper rounding at the end. It is recommended that all your calculations be done using Excel as this software is always using many decimal places in all calculations. Once you have the final answer, just round it properly.

Question 1. Credit cards market segmentation [ 24 marks]

A new credit card company operating in Canada is investigating various market segments to determine their profitability. One of the segments of interest is that of immigrants who became permanent residents in Canada in 2022. The latest report from IRCC shows that this population amount to 431,64512 individuals and they would like to know how many of them don’t use a credit card to pay for the good and services they purchase. They commission a random survey of 500 individuals in this population to investigate their usual payment practice and obtain the following summary results: cash (98); check (47); Visa (165); Master card (151) and other credit cards (39).

a) [8 marks] The company will hold on to this market segment if more than 25% (1 out of 4 individuals) currently use cash or check as a payment method. Test at 5% level of significance whether the proportion of immigrants who became permanent residents in Canada in 2022 and who use cash or check as a payment method meets the company’s threshold for targeting this market segment. Use both critical value and p-value approach showing all the steps of hypotheses (hypotheses, decision region, test statistic, conclusion with justification). (Manual Calculations)

b) [2 marks] Are the assumptions/conditions for the above test satisfied?

c) [4 marks] Calculate manually an appropriate one-sided 95% confidence interval [HINT: lower bound] for the population proportion of immigrants who became permanent residents in Canada in 2022 and who use cash or check as a payment method. Interpret the confidence interval. Does this interval allow you to make the same conclusion as in part a) above? Explain. (Manual Calculations)

d) [3 marks] Using a two-sided 95% confidence interval for the population proportion of immigrants who became permanent residents in Canada in 2022 and who use cash or check as a payment method, calculate an estimate of the size of this market segment. [HINT: calculate a range of values rounded to the nearest thousand for the estimate]

e) [4 marks] The company’s senior management would like a more precise range estimate of the size for this market segment to strengthen their business case and they are prepared to commission a larger survey. How large sample size would be needed to estimate, within 2%, the true proportion with 90% confidence? What would be a new estimate of the size of this market segment (rounded to the nearest thousand) assuming the new survey would obtain the same p^? [HINT: Assume that the original survey (500 individuals) provide is a reasonable estimate of p^.] (Manual Calculations)

f) [3 marks] You are surprised to note that the company’s survey reported 29% of immigrants still using cash or check as a payment method and you would like to check if that is the case at uOttawa. Suppose you were able to draw a random sample of 25 uOttawa students who became permanent residents in 2022 and found only 2 using cash or check as a payment method. Test whether this would be sufficient evidence to indicate that the proportion of immigrants who became permanent residents in 2022 and are using cash or check as a payment method among uOttawa students is less than the 29%. Use a 2% level of significance and show how you would calculate the p-value for this test.

Question 2. Teleworking Practices [ 22 marks]

A labour union representing public sector employees is claiming that the recent government 2-day a week in-person presence in office directive is not in line with current practices in the private sector. They have commissioned a national survey to compare teleworking policies between similar public and private sector employers. The survey looked at two independent random samples of employers: 110 and 140 in the public and private sectors respectively. They found that 73 public sector employers impose a 2-day per week presence in office compared to 75 for private sector employers.

a) [12 marks] Test whether employers in these two sectors are equally likely to impose a 2-day per week presence in office. Use the critical value and p-value approach and a 5% level of significance. Make sure to include all the steps of hypotheses (hypotheses, decision zone, critical value and p-value, conclusion with justification). Show your manual calculations and provide a StatCrunch output confirming your results. [Hint: let p1 be the proportion of public sector and p2 the proportion of private sector employers who impose a 2-day per week presence in office]. (Manual calculations and StatCrunch)

b) [8 marks] Calculate and interpret an appropriate 95% confidence interval for the true difference between the proportions of public sector and private sector employers who impose a 2-day per week presence in office. Show your Excel or StatCrunch output for verification. (Manual calculations and StatCrunch)

c) [2 marks] Explain how your conclusions in parts a) and b) above are consistent.

Question 3. Property Assessment Values [ 23 marks]

The file Assign1Data.xlsx contains property assessment values in dollars (1695 records) originating from the property assessment roll of one small town in Ontario.

a) [1 mark] Treating this set of data as population data, use Excel or StatCrunch to calculate the population mean and population standard deviation for the ‘Property value’ variable.

b) [3 marks] Examine a histogram and boxplot of this variable and explain if the means of all possible random samples of size 50 from this population would form a normal distribution.

c) [7 marks] A random sample of 15 property values has been drawn using the Sampling function in the Excel Analysis ToolPak and displayed in the sheet Size 15 Sample in the Assign1Data file. Use this sample to test whether the population mean is different from the value calculated in part a) above. Use the critical value and the p-value approach and a 5% level of significance. Assume that the population standard deviation is unknown, and the shape of the population property assessment values follows Normal distribution, notwithstanding your answer to part b). Make sure to include all the steps of hypotheses (hypotheses, decision zone, critical value, p-value, conclusion with justification) and show your manual calculations.

d) [5 marks] Using the same sample as in part c) above, build a 95% confidence interval for the population mean. Does the interval include the population mean calculated in part a) above? Explain why or why not.

e) [2 marks] Would you have the same conclusion in part c) above, if you had chosen a 1% level of significance? Use Excel or StatCrunch for the test and show your output to justify your answer.

f) [5 marks] Now, use the Excel Analysis ToolPak or StatCrunch sampling routine3 to draw 25 samples of size n = 50 from the population data. Report the 25 means of these samples. Calculate the mean and standard deviation of these sample means and compare the results with the mean and standard deviation of the population obtained in a) above? Are they of equal values? Explain.