The health authority produced a second set of samples but this time they wanted to take into account that another potentially major factor in the analysis could be the hospitals from which the patients are being transferred. They took two samples of size 45 (from the complete data set with all lengths of stay included) but this time they made sure that for each patient at hospital x who was transferred to "Chronic Care" there was also a patient from that same hospital in the other sample who was transferred to a "home for the aged". The Minitab output below shows the data and some partial analyses. Descriptive Statistics: Chronic Care Home for the Aged Difference N 45 45 45 Mean 27.44 41.44 -14.00 St Dev 24.81 31.57 34.39 SE Mean 3.70 4.71 5.13 Wilcoxon Signed Rank Test: Differences Test of median = 0.000000 versus median not = 0.000000 N for Wilcoxon N Test Statistic P Differences 45 45 277.0 0.007 Estimated Median -14.00 Mann-Whitney Test and CI: Chronic Care, Home for the Aged N Median Chronic Care 45 19.00 Home for the Aged 45 30.00 Point estimate for ETA1-ETA2 is -12.00 95.0 Percent CI for ETA1-ETA2 is (-19.00,-4.00) W = 1707.5 Test of ETA1 ETA2 Vs ETAl not = ETA2 is significant at 0.0062 The test is significant at 0.0061 (adjusted for ties) (a) Explain the nature of the appropriate test. Should the test be based on independent or paired samples? Explain briefly. [2 marks] (b) Given your answer in (a), is the appropriate test a parametric or a non-parametric test? Please make reference to specific boxplots in your answer. [2 marks] (c) Notwithstanding your answer in (b), perform an appropriate parametric test to determine whether there is sufficient evidence of a difference in the average lengths of stay at the 0.05 significance level. Use the p- value approach. [4 marks] (d) Now calculate a 95% confidence interval for the average difference in hospital stays between transfers to "Chronic Care" versus a "home for the aged. [2 marks] The health authority produced a second set of samples but this time they wanted to take into account that another potentially major factor in the analysis could be the hospitals from which the patients are being transferred. They took two samples of size 45 (from the complete data set with all lengths of stay included) but this time they made sure that for each patient at hospital x who was transferred to "Chronic Care" there was also a patient from that same hospital in the other sample who was transferred to a "home for the aged". The Minitab output below shows the data and some partial analyses. Descriptive Statistics: Chronic Care Home for the Aged Difference N 45 45 45 Mean 27.44 41.44 -14.00 St Dev 24.81 31.57 34.39 SE Mean 3.70 4.71 5.13 Wilcoxon Signed Rank Test: Differences Test of median = 0.000000 versus median not = 0.000000 N for Wilcoxon N Test Statistic P Differences 45 45 277.0 0.007 Estimated Median -14.00 Mann-Whitney Test and CI: Chronic Care, Home for the Aged N Median Chronic Care 45 19.00 Home for the Aged 45 30.00 Point estimate for ETA1-ETA2 is -12.00 95.0 Percent CI for ETA1-ETA2 is (-19.00,-4.00) W = 1707.5 Test of ETA1 ETA2 Vs ETAl not = ETA2 is significant at 0.0062 The test is significant at 0.0061 (adjusted for ties) (a) Explain the nature of the appropriate test. Should the test be based on independent or paired samples? Explain briefly. [2 marks] (b) Given your answer in (a), is the appropriate test a parametric or a non-parametric test? Please make reference to specific boxplots in your answer. [2 marks] (c) Notwithstanding your answer in (b), perform an appropriate parametric test to determine whether there is sufficient evidence of a difference in the average lengths of stay at the 0.05 significance level. Use the p- value approach. [4 marks] (d) Now calculate a 95% confidence interval for the average difference in hospital stays between transfers to "Chronic Care" versus a "home for the aged. [2 marks]
