Statistics Paper

1. Consider this hypothesis test:

H₀: p₁ - p₂ = 0

H_a: p₁ - p₂ < 0

Here p₁ is the population mean of Population 1 and p₂ is the population proportion of Population 2. Use the statistics summarized from a simple random sample of each of the two populations to complete the following:

1. What is the pooled estimate of p?
2. Compute the test statistic z
3. What is the rejection rule using the critical value approach and α=0.05
4. Based on the rejection rule from c., what is your conclusion on the hypotheses?
5. What is the p-value?
6. Use the above data to construct a 95% confidence interval for p₁ - p₂

2. Partial responses from an employee satisfaction survey for two regions of a mid-size IT firm were recorded in the attached BUSI1013-Two Sample Proportions.XLSX file. These responses are answers by a simple random sample of employees from the two regions to the question: Are you planning to stay with the company one year from now (Yes or No).  The firm wants to use this data to test the research (alternative) hypothesis that the proportion of employees within the two regions who plan to stay with the company one year from now is not the same. The null hypothesis is that the proportion of employees within the two regions who plan to stay with the company one year from now is the same.

1. What are the sample proportion for the two regions
2. Compute the test statistic z used to test the hypotheses
3. Can the firm conclude that the proportion of employees within the two regions who plan to stay with the company one year from now is not the same? Use the p-value approach and α=0.05 to test the hypotheses stated above
4. Construct a 95% confidence interval for the difference of the population proportion for the two regions

3.Use BUSI1013-Case.xls and the description of this file  to answer this question.

Description:

You have just been promoted to the position of Director of Marketing of OYCU, one of the large credit unions in Ontario. As your first assignment, you have been given the job of revamping the Member Service function at the branches – customers at the credit union are called members. Your predecessor had started the work through a pilot study at a number of branches with a follow-up market research study to assess the effectiveness of the pilot.

Essentially, the pilot involves the establishment of the Personal Financial Well-Being Advisor (PFWA) concept.  PFWA were selected on the basis of professional qualification such as CFP, superior performance, and years of experience with the OYCU. They were then assigned to serve exclusively a group of active members at these branches. Through this highly personalized service offering, it is expected that banking relationship with these members will be deepened resulting in increases of personal deposits and/or loans from them.

1. Perform a statistical test to see whether the proportion of members who would recommend the Credit Union to their family and friends have increased as a result of the pilot,
2. Construct a 90% confidence interval for the difference of the proportions, before and after the pilot, of members who would recommend the Credit Union to their family and friends

4.  The following table contains observed frequencies for a sample of 100

1. What is the expected frequency for the “B and Category 2” cell?
2. Calculate the chi square statistic
3. What is the rejection rule using the critical value approach and α=0.05
4. What can you say about the  independence of the row and column variables

5.  A national accounting firm have completed an internal survey on its education leave policies. The key question in the survey is whether or not the existing education leave policy is adequate for all employees. The following is the output of a statistical analysis of the data:

Based on this output, can the firm conclude that the opinion on the education policy is dependent on the level of management of the employees? Use a chi square test and a level of significance of 0.05.

6. Use BUSI1013-Case.xls and the description of this file  to perform a statistical test on whether or not a member would recommend the Credit Union to their family and friends after the pilot is dependent on the gender of the member.

Description:

You have just been promoted to the position of Director of Marketing of OYCU, one of the large credit unions in Ontario. As your first assignment, you have been given the job of revamping the Member Service function at the branches – customers at the credit union are called members. Your predecessor had started the work through a pilot study at a number of branches with a follow-up market research study to assess the effectiveness of the pilot.

Essentially, the pilot involves the establishment of the Personal Financial Well-Being Advisor (PFWA) concept.  PFWA were selected on the basis of professional qualification such as CFP, superior performance, and years of experience with the OYCU. They were then assigned to serve exclusively a group of active members at these branches. Through this highly personalized service offering, it is expected that banking relationship with these members will be deepened resulting in increases of personal deposits and/or loans from them.