A new credit card company operating in Canada is investigating various market segments to determine their...

  

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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 ] (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 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 ] (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

Answer rating: 100% (QA)

Part a Hypothesis Test for Proportion of Immigrants Using Cash or Check Hypotheses H0 The proportion of immigrants who became permanent residents in Canada in 2022 and use cash or check as a payment m... View the full answer