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Companies are concerned with the quality of their customer service as this is often highly correlated with profitability. The following satisfaction scores of three companies for the fourth quarters of two consecutive years were obtained from the American Customer Satisfaction Index. Assume that the scores are based on a poll of 61 customers from each company. Historical polling data suggest that the standard deviation can be assumed to equal seven points in each case. Company Company 1 Company 2 Company 3 Current Year Hi Uy - Uy #0 H:4 - 4 = 0 72 81 79 Previous Year 76 84 (a) For Company 1, is the decrease in the satisfaction score over these two years statistically significant? Use a = 0.05. (Let u, be the population mean satisfaction score for the current year, and let u, be the population mean satisfaction score for the previous year.) State the null and alternative hypotheses. OHH H 0 HH > 0 Hoi Uy - U220 H: H H <0 81 : - <0 HH-420 H: H H = 0 HH H #0 Calculate the test statistic. (Use - . Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = What can you conclude? O Do not reject Ho. There is sufficient evidence to conclude that customer service has worsened for Company 1. O Reject Ho. There is sufficient evidence to conclude that customer service has worsened for Company 1. O Reject Ho. There is not sufficient evidence to conclude that customer service has worsened for Company 1. O Do not reject Ho. There is not sufficient evidence to conclude that customer service has worsened for Company 1. (b) Can you conclude that the current year score for Company 1 is below the retail sector's national average of 76.9? Use a = 0.05. State the null and alternative hypotheses. H: #76.9 H = 76.9 O Ho: 76.9 (b) Can you conclude that the current year score for Company 1 is below the retail sector's national average of 76.9? Use a = 0.05. State the null and alternative hypotheses. H: = 76.9 H: = 76.9 OH: 76.9 H:4> 76.9 OH: 76.9 H: <76.9 O Ho: = 76.9 H:#76.9 OH: > 76.9 H: 76.9 Calculate the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = What can you conclude? O Reject Ho. There is not sufficient evidence to conclude that Company 1's customer satisfaction score is significantly below the national average. O Do not reject Ho. There is not sufficient evidence to conclude that Company 1's customer satisfaction score is significantly below the national average. O Reject Ho. There is sufficient evidence to conclude that Company 1's customer satisfaction score is significantly below the national average. O Do not reject H. There is sufficient evidence to conclude that Company 1's customer satisfaction score is significantly below the national average. (c) For Company 2, is the decrease over these two years statistically significant? Use a = 0.05. (Let u, be the population mean satisfaction score for the current year, and let u, be the population mean satisfaction score for the previous year.) State the null and alternative hypotheses. Hi Hi-H250 HH H > 0 OH:4-4 0 H H - H <0 O Ho: M - 40 H: H - H = 0 - H: H H 20 H: H - H = 0 Calculate the test statistic. (Use -. Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value= What can you conclude? O Reject Ho. There is not sufficient evidence to conclude that customer service has worsened for Company 2. O Reject Ho. There is sufficient evidence to conclude that customer service has worsened for Company 2. O Do not reject Ho. There is not sufficient evidence to conclude that customer service has worsened for Company 2. O Do not reject Ho. There is sufficient evidence to conclude that customer service has worsened for Company 2. (d) When conducting a hypothesis test with the values given for the standard deviation, sample size, and a, how large must the decrease over these two years be for it to be statistically significant? (Enter your answer as a positive number. Round your answer to two decimal places.) The difference between the two satisfaction scores must be at least for the decrease to be statistically significant. (e) Use the result of part (d) to state whether the decrease for Company 3 over these two years is statistically significant. O The difference between the previous and current years' satisfaction scores is less than the minimum difference found in part (d), so the decrease is statistically significant. O The difference between the previous and current years' satisfaction scores is greater than the minimum difference found in part (d), so the decrease is statistically significant. O The difference between the previous and current years' satisfaction scores is less than the minimum difference found in part (d), so the decrease is not statistically significant. O The difference between the previous and current years' satisfaction scores is greater than the minimum difference found in part (d), so the decrease is not statistically significant. Companies are concerned with the quality of their customer service as this is often highly correlated with profitability. The following satisfaction scores of three companies for the fourth quarters of two consecutive years were obtained from the American Customer Satisfaction Index. Assume that the scores are based on a poll of 61 customers from each company. Historical polling data suggest that the standard deviation can be assumed to equal seven points in each case. Company Company 1 Company 2 Company 3 Current Year Hi Uy - Uy #0 H:4 - 4 = 0 72 81 79 Previous Year 76 84 (a) For Company 1, is the decrease in the satisfaction score over these two years statistically significant? Use a = 0.05. (Let u, be the population mean satisfaction score for the current year, and let u, be the population mean satisfaction score for the previous year.) State the null and alternative hypotheses. OHH H 0 HH > 0 Hoi Uy - U220 H: H H <0 81 : - <0 HH-420 H: H H = 0 HH H #0 Calculate the test statistic. (Use - . Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = What can you conclude? O Do not reject Ho. There is sufficient evidence to conclude that customer service has worsened for Company 1. O Reject Ho. There is sufficient evidence to conclude that customer service has worsened for Company 1. O Reject Ho. There is not sufficient evidence to conclude that customer service has worsened for Company 1. O Do not reject Ho. There is not sufficient evidence to conclude that customer service has worsened for Company 1. (b) Can you conclude that the current year score for Company 1 is below the retail sector's national average of 76.9? Use a = 0.05. State the null and alternative hypotheses. H: #76.9 H = 76.9 O Ho: 76.9 (b) Can you conclude that the current year score for Company 1 is below the retail sector's national average of 76.9? Use a = 0.05. State the null and alternative hypotheses. H: = 76.9 H: = 76.9 OH: 76.9 H:4> 76.9 OH: 76.9 H: <76.9 O Ho: = 76.9 H:#76.9 OH: > 76.9 H: 76.9 Calculate the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = What can you conclude? O Reject Ho. There is not sufficient evidence to conclude that Company 1's customer satisfaction score is significantly below the national average. O Do not reject Ho. There is not sufficient evidence to conclude that Company 1's customer satisfaction score is significantly below the national average. O Reject Ho. There is sufficient evidence to conclude that Company 1's customer satisfaction score is significantly below the national average. O Do not reject H. There is sufficient evidence to conclude that Company 1's customer satisfaction score is significantly below the national average. (c) For Company 2, is the decrease over these two years statistically significant? Use a = 0.05. (Let u, be the population mean satisfaction score for the current year, and let u, be the population mean satisfaction score for the previous year.) State the null and alternative hypotheses. Hi Hi-H250 HH H > 0 OH:4-4 0 H H - H <0 O Ho: M - 40 H: H - H = 0 - H: H H 20 H: H - H = 0 Calculate the test statistic. (Use -. Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value= What can you conclude? O Reject Ho. There is not sufficient evidence to conclude that customer service has worsened for Company 2. O Reject Ho. There is sufficient evidence to conclude that customer service has worsened for Company 2. O Do not reject Ho. There is not sufficient evidence to conclude that customer service has worsened for Company 2. O Do not reject Ho. There is sufficient evidence to conclude that customer service has worsened for Company 2. (d) When conducting a hypothesis test with the values given for the standard deviation, sample size, and a, how large must the decrease over these two years be for it to be statistically significant? (Enter your answer as a positive number. Round your answer to two decimal places.) The difference between the two satisfaction scores must be at least for the decrease to be statistically significant. (e) Use the result of part (d) to state whether the decrease for Company 3 over these two years is statistically significant. O The difference between the previous and current years' satisfaction scores is less than the minimum difference found in part (d), so the decrease is statistically significant. O The difference between the previous and current years' satisfaction scores is greater than the minimum difference found in part (d), so the decrease is statistically significant. O The difference between the previous and current years' satisfaction scores is less than the minimum difference found in part (d), so the decrease is not statistically significant. O The difference between the previous and current years' satisfaction scores is greater than the minimum difference found in part (d), so the decrease is not statistically significant.
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Management Accounting Information for Decision-Making and Strategy Execution
ISBN: 978-0137024971
6th Edition
Authors: Anthony A. Atkinson, Robert S. Kaplan, Ella Mae Matsumura, S. Mark Young
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