Management: Most selling organizations have many accounts they track in one form or another. All of those clients and prospects typically have designations of some type applied to them in territory and account planning. They are differentiated by size, vertical market, geographic location, commercial vs. public sector, etc. An American multinational technology company headquartered in Armonk, New York, with operations in over 170 countries that produces and sells computer hardware, middleware, and software, and provides hosting and consulting services in areas ranging from mainframe computers to nanotechnology adopted an account classification system three decades ago. The company routinely classifies accounts into one of these four categories: Keep: Accounts we definitely want to retain. These aren't necessarily the largest or most prestigious accounts, but they are core accounts that are consistent and relatively easy to manage. Attain: Our ideal accounts that match our target profile, those that we aspire to win. They fit the description of, 'We do not work with them now but, we would like to. Recapture: Previously active accounts that are worthy of the time and resources needed to woo them back. There are many reasons accounts go cold, which are not always tied to performance, but we would like to work with them again. Expand: Accounts in which we see great potential for expansion and those in which we are willing, and often eager, to invest in. The CEO of the company has an ambitious plan to meet the targets summarized in the table below. In order to evaluate whether or not the company has accomplished this goal last quarter, the Data Science Division (DSD) took a random sample of 80 accounts from last quarter. These data are also summarized in the table below. Account Type CEO's Target % Observed count Keep 45% 29 Attain 15% 19 Recapture 15% 13 Expand 25% 19 Conduct the proper hypothesis test to determine if the company achieved the CEO's goal last quarter. Use a = 0.10. (a) What is the name of the appropriate statistical test? O The Chi-Square Goodness of Fit Test The Chi-Square Test of Independence O The z-Test for Single Population Proportion The t-Test for a Single Population Mean O The Paired t-Test The 2 Independent Samples t-Test Justify your choice from immediately above. The variable of interest (Account Type) is quantitative in nature, however, the same funds were measured twice; therefore the data are paired. As a result, the paired t-test is appropriate. The variable of interest (Account Type) is categorical and multinomial in nature. Therefore, the most natural summary is multiple proportions. The main goal is to compare the sample data to a historical or baseline trend or pattern. As a result, the Chi-Square Goodness of Fit Test is appropriate. The variable of interest (Account Type) is quantitative in nature and therefore the most natural summary statistic is a mean. Furthermore, the data consist of only 1 independent sample. Therefore, the t-test for single population mean is appropriate. The variable of interest (Account Type) is quantitative in nature and the data consist of two independent samples. The main goal is to compare their group outcomes. As a result, the 2 independent samples t-test is appropriate. The variable of interest (Account Type) is categorical and binary in nature and therefore the most natural summary statistic is a proportion. Furthermore, the data consist of only 1 independent sample. Therefore, the z-test for single population proportion is appropriate. There are two variables of interest and they are both categorical in nature. The main goal is to test whether or not the two variables are independent of each other. As a result, the Chi-Square Test of Independence is appropriate. What is the population of interest in this scenario? The 80 accounts that were chosen All targets last quarter The 80 targets that were chosen O All accounts last quarter What is the population parameter? n1, n2...., 14 = The observed counts of the 80 accounts in each category that were chosen O p = The proportion of the 80 accounts that were chosen O P1, P2..., P4 = The proportion of all accounts last quarter in each category O p = The proportion of all accounts last quarter What is the sample? All accounts last quarter O All targets last quarter The 80 targets that were chosen The 80 accounts that were chosen What is the sample statistic? O p = The proportion of the 80 accounts that were chosen Op = The proportion of all accounts last quarter O P1, P2,..., P4 = The proportion of all accounts last quarter in each category Oni, n2...., 14 The observed counts of the 80 accounts in each category that were chosen (b) State the hypotheses to be tested. O Ho: These two variables are independent. Ha: These two variables are not independent. O Ho: P1 = P2 = P3 = P4 = 1/4. Ha: At least one of the proportions is not equal to 1/4. O Ho: P1 = 0.45, P2 = 0.15, P3 = 0.15, P4 = 0.25. Ha: At least one of the proportions is different. O Ho: P1 = 0.45, P2 = 0.15, P3 = 0.15, P4 = 0.25. Ha: All of the proportions are different. Interpret the hypotheses you specified above. O Ho: The distribution of account types is consistent with the CEO's goal. Ha: The distribution of account types is NOT consistent with the CEO's goal. O Ho: The account types are equally distributed; therefore, consistent with the CEO's goal. Ha: The account types are NOT equally distributed; therefore, inconsistent with the CEO's goal. O Ho: The account types are NOT equally distributed; therefore, inconsistent with the CEO's goal. Ha: The account types are equally distributed; therefore, inconsistent with the CEO's goal. O Ho: The distribution of account types is NOT consistent with the CEO's goal. Ha: The distribution of account types is consistent with the CEO's goal. (c) State the decision rule. Reject Ho if p > 0.05. Do not reject Ho if p 0.05. Reject Ho if p > 0.10. Do not reject Ho if p 0.10. Calculate the expected count for each category: (Enter your answer to three decimal places.) Keep : Attain : Recapture : Expand : Select all conditions/assumptions that are applicable for this test (Not whether or not they have been met, just identify the appropriate conditions/assumptions of this test). (Select all that apply.) The sample was randomly chosen. The analysis units are meaningfully paired in some way. The 10% condition is met. The data consist of 2 independent samples. The nearly normal condition is met. None of the conditions are met. The analysis units (i.e., the accounts) are independent. The expected count is at least 5 for every cell. The data are count data. (d) Calculate the contribution to the test statistic for the 'Recapture' account type. (Enter your answer to three decimal places.) The full test statistic value is 5.578. State the appropriate test statistic name, degrees of freedom, test statistic value, and the associated p-value (Enter your degrees of freedom as a whole number, the test statistic value to three decimal places, and the p-value to four decimal places). ---Select-- p --Select-- Interpret the p-value you calculated immediately above by mentally inserting the p-value in the blanks below. There is a probability of obtaining the test results that we obtained here or more extreme from a sample of 80 if the Ho is true and the CEO's goal has been reached. O There is a probability of obtaining the test results that we obtained here or more extreme from a sample of 80 if the Ho is false and the variables are related. There is a probability of obtaining the test results that we obtained here or more extreme from a sample of 80 if the Ho is false and the CEO's goal has been reached. There is a probability of obtaining the test results that we obtained here or more extreme from a sample of 80 if the Ho is true and the variables are independent. (e) State your conclusions. The results are NOT statistically significant at the 10% level. There is sufficient evidence to conclude that the company has NOT achieved the CEO's goal. The results are statistically significant at the 10% level. It is plausible that the CEO's goal has been met.. The results are NOT statistically significant at the 10% level. It is plausible that the CEO's goal has been met. The results are statistically significant at the 10% level. There is sufficient evidence to conclude that the company has NOT achieved the CEO's goal. (f) Compute the residual for the 'Recapture' account type. (Enter your answer to three decimal places.) (f) Compute the residual for the 'Recapture' account type. (Enter your answer to three decimal places.) Interpret the residual for the 'Recapture' account type you calculated immediately above by mentally inserting the ABSOLUTE VALUE of that number in the blanks below. standard deviation(s) above the number of 13 Recapture accounts we would expect if The observed number of 12.000 Recapture accounts is the Ho were false. The observed number of 12.000 Recapture accounts is the Ho were true. standard deviation(s) above the number of 13 Recapture accounts we would expect if standard deviation(s) above the number of 12.000 Recapture accounts we would expect if The observed number of 13 Recapture accounts is the Ho were false. The observed number of 13 Recapture accounts is the Ho were true. standard deviation(s) above the number of 12.000 Recapture accounts we would expect if Management: Most selling organizations have many accounts they track in one form or another. All of those clients and prospects typically have designations of some type applied to them in territory and account planning. They are differentiated by size, vertical market, geographic location, commercial vs. public sector, etc. An American multinational technology company headquartered in Armonk, New York, with operations in over 170 countries that produces and sells computer hardware, middleware, and software, and provides hosting and consulting services in areas ranging from mainframe computers to nanotechnology adopted an account classification system three decades ago. The company routinely classifies accounts into one of these four categories: Keep: Accounts we definitely want to retain. These aren't necessarily the largest or most prestigious accounts, but they are core accounts that are consistent and relatively easy to manage. Attain: Our ideal accounts that match our target profile, those that we aspire to win. They fit the description of, 'We do not work with them now but, we would like to. Recapture: Previously active accounts that are worthy of the time and resources needed to woo them back. There are many reasons accounts go cold, which are not always tied to performance, but we would like to work with them again. Expand: Accounts in which we see great potential for expansion and those in which we are willing, and often eager, to invest in. The CEO of the company has an ambitious plan to meet the targets summarized in the table below. In order to evaluate whether or not the company has accomplished this goal last quarter, the Data Science Division (DSD) took a random sample of 80 accounts from last quarter. These data are also summarized in the table below. Account Type CEO's Target % Observed count Keep 45% 29 Attain 15% 19 Recapture 15% 13 Expand 25% 19 Conduct the proper hypothesis test to determine if the company achieved the CEO's goal last quarter. Use a = 0.10. (a) What is the name of the appropriate statistical test? O The Chi-Square Goodness of Fit Test The Chi-Square Test of Independence O The z-Test for Single Population Proportion The t-Test for a Single Population Mean O The Paired t-Test The 2 Independent Samples t-Test Justify your choice from immediately above. The variable of interest (Account Type) is quantitative in nature, however, the same funds were measured twice; therefore the data are paired. As a result, the paired t-test is appropriate. The variable of interest (Account Type) is categorical and multinomial in nature. Therefore, the most natural summary is multiple proportions. The main goal is to compare the sample data to a historical or baseline trend or pattern. As a result, the Chi-Square Goodness of Fit Test is appropriate. The variable of interest (Account Type) is quantitative in nature and therefore the most natural summary statistic is a mean. Furthermore, the data consist of only 1 independent sample. Therefore, the t-test for single population mean is appropriate. The variable of interest (Account Type) is quantitative in nature and the data consist of two independent samples. The main goal is to compare their group outcomes. As a result, the 2 independent samples t-test is appropriate. The variable of interest (Account Type) is categorical and binary in nature and therefore the most natural summary statistic is a proportion. Furthermore, the data consist of only 1 independent sample. Therefore, the z-test for single population proportion is appropriate. There are two variables of interest and they are both categorical in nature. The main goal is to test whether or not the two variables are independent of each other. As a result, the Chi-Square Test of Independence is appropriate. What is the population of interest in this scenario? The 80 accounts that were chosen All targets last quarter The 80 targets that were chosen O All accounts last quarter What is the population parameter? n1, n2...., 14 = The observed counts of the 80 accounts in each category that were chosen O p = The proportion of the 80 accounts that were chosen O P1, P2..., P4 = The proportion of all accounts last quarter in each category O p = The proportion of all accounts last quarter What is the sample? All accounts last quarter O All targets last quarter The 80 targets that were chosen The 80 accounts that were chosen What is the sample statistic? O p = The proportion of the 80 accounts that were chosen Op = The proportion of all accounts last quarter O P1, P2,..., P4 = The proportion of all accounts last quarter in each category Oni, n2...., 14 The observed counts of the 80 accounts in each category that were chosen (b) State the hypotheses to be tested. O Ho: These two variables are independent. Ha: These two variables are not independent. O Ho: P1 = P2 = P3 = P4 = 1/4. Ha: At least one of the proportions is not equal to 1/4. O Ho: P1 = 0.45, P2 = 0.15, P3 = 0.15, P4 = 0.25. Ha: At least one of the proportions is different. O Ho: P1 = 0.45, P2 = 0.15, P3 = 0.15, P4 = 0.25. Ha: All of the proportions are different. Interpret the hypotheses you specified above. O Ho: The distribution of account types is consistent with the CEO's goal. Ha: The distribution of account types is NOT consistent with the CEO's goal. O Ho: The account types are equally distributed; therefore, consistent with the CEO's goal. Ha: The account types are NOT equally distributed; therefore, inconsistent with the CEO's goal. O Ho: The account types are NOT equally distributed; therefore, inconsistent with the CEO's goal. Ha: The account types are equally distributed; therefore, inconsistent with the CEO's goal. O Ho: The distribution of account types is NOT consistent with the CEO's goal. Ha: The distribution of account types is consistent with the CEO's goal. (c) State the decision rule. Reject Ho if p > 0.05. Do not reject Ho if p 0.05. Reject Ho if p > 0.10. Do not reject Ho if p 0.10. Calculate the expected count for each category: (Enter your answer to three decimal places.) Keep : Attain : Recapture : Expand : Select all conditions/assumptions that are applicable for this test (Not whether or not they have been met, just identify the appropriate conditions/assumptions of this test). (Select all that apply.) The sample was randomly chosen. The analysis units are meaningfully paired in some way. The 10% condition is met. The data consist of 2 independent samples. The nearly normal condition is met. None of the conditions are met. The analysis units (i.e., the accounts) are independent. The expected count is at least 5 for every cell. The data are count data. (d) Calculate the contribution to the test statistic for the 'Recapture' account type. (Enter your answer to three decimal places.) The full test statistic value is 5.578. State the appropriate test statistic name, degrees of freedom, test statistic value, and the associated p-value (Enter your degrees of freedom as a whole number, the test statistic value to three decimal places, and the p-value to four decimal places). ---Select-- p --Select-- Interpret the p-value you calculated immediately above by mentally inserting the p-value in the blanks below. There is a probability of obtaining the test results that we obtained here or more extreme from a sample of 80 if the Ho is true and the CEO's goal has been reached. O There is a probability of obtaining the test results that we obtained here or more extreme from a sample of 80 if the Ho is false and the variables are related. There is a probability of obtaining the test results that we obtained here or more extreme from a sample of 80 if the Ho is false and the CEO's goal has been reached. There is a probability of obtaining the test results that we obtained here or more extreme from a sample of 80 if the Ho is true and the variables are independent. (e) State your conclusions. The results are NOT statistically significant at the 10% level. There is sufficient evidence to conclude that the company has NOT achieved the CEO's goal. The results are statistically significant at the 10% level. It is plausible that the CEO's goal has been met.. The results are NOT statistically significant at the 10% level. It is plausible that the CEO's goal has been met. The results are statistically significant at the 10% level. There is sufficient evidence to conclude that the company has NOT achieved the CEO's goal. (f) Compute the residual for the 'Recapture' account type. (Enter your answer to three decimal places.) (f) Compute the residual for the 'Recapture' account type. (Enter your answer to three decimal places.) Interpret the residual for the 'Recapture' account type you calculated immediately above by mentally inserting the ABSOLUTE VALUE of that number in the blanks below. standard deviation(s) above the number of 13 Recapture accounts we would expect if The observed number of 12.000 Recapture accounts is the Ho were false. The observed number of 12.000 Recapture accounts is the Ho were true. standard deviation(s) above the number of 13 Recapture accounts we would expect if standard deviation(s) above the number of 12.000 Recapture accounts we would expect if The observed number of 13 Recapture accounts is the Ho were false. The observed number of 13 Recapture accounts is the Ho were true. standard deviation(s) above the number of 12.000 Recapture accounts we would expect if