(a) (b) (20 points) Comment on Jimmy and Kim's experiment design. Is there anything that could...

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(a) (b) (20 points) Comment on Jimmy and Kim's experiment design. Is there anything that could be improved to help their case? 4 (50 points) Fill in the partial ANOVA table below and compute a p-value for the one-way ANOVA. What hypotheses are being tested, and what is the conclusion? source factor error SS DF MS F total 118.70 (c) (50 points) Differing in their approach to statistical analysis, Jimmy and Kim wrote separate reports with their own conclusions, shown in Appendix 1 and 2, respectively. Whose analysis do you agree with, and why? Make sure to justify your conclusions! (d) (25 points) What advice do you have for Jimmy and Kim at this point? Is there any way to salvage the case? Appendix 1 Analysis by James McGill, Esq. As part of ongoing litigation against Sandpiper Crossing, LLC (referred to hereafter as DEFENDANT), the law office of Wexler-McGill, representing the residents of Sandpiper Crossing (referred to hereafter as CLIENT) conducted an experiment to prove that DEFENDANT has knowingly, systematically, and maliciously overcharged CLIENT, with damages estimated in the millions of dollars. We compared estimates for the population mean charge for a standard service across four comparable retirement facilities across the greater Albuquerque, NM area. Our collected data, summarized in Figure 3, clearly illustrate the malice with which DEFENDANT overcharged CLIENT. To support our case, we conducted pairwise t-tests, which test for statistically significant differences in population means. The tests and our conclusions are shown below. Test 1: Ho PSP PABQGL H PSP PABQCL (1) (2) where sp refers to the population mean service charge at Sandpiper Crossing, and #ABQGL refers to the population mean service charge at ABQ Grand Living. In this test, we reject Ho with p-value = 0.04 < 0.05, and therefore conclude that the service charge at Sandpiper Crossing is significantly different than the charge for the same service at ABQ Grand Living. Test 2: Ho: H: PSP=PPL PSP PL (3) (4) where #sp refers to the population mean service charge at Sandpiper Crossing, and #PL refers to the population mean service charge at Paloma Landing. In this test, we reject Ho with p-value = 0.03 < 0.05, and therefore conclude that the service charge at Sandpiper Crossing is significantly different than the charge for the same service at Paloma Landing. Test 3: Ho: H: PSP=PM PSP #PM (5) (6) where sp refers to the population mean service charge at Sandpiper Crossing, and M refers to the popula- tion mean service charge at The Montebello Landing. In this test, we reject Ho with p-value = 0.02 < 0.05, and therefore conclude that the service charge at Sandpiper Crossing is significantly different than the charge for the same service at The Montebello. As the court can see, in all cases the service charge at Sandpiper Crossing is significantly different than the charge at a comparable retirement facility, and in fact the charge is systematically higher across all tests. This proves that DEFENDANT is guilty of systematically overcharging CLIENT, and we ask the court for the maximum damages allowed by law. Appendix 2 Analysis by Kimberly Wexler, Esq. As part of ongoing litigation against Sandpiper Crossing, LLC (referred to hereafter as DEFENDANT), the law office of Wexler-McGill, representing the residents of Sandpiper Crossing (referred to hereafter CLIENT) conducted an experiment to prove that DEFENDANT has knowingly, systematically, and maliciously overcharged CLIENT, with damages estimated in the millions of dollars. We compared estimates for the population mean charge for a standard service across four comparable retirement facilities across the greater Albuquerque, NM area. Our collected data, summarized in Figure 3, show that although the sample mean service charge is indeed higher at DEFENDANT's facility, they do not necessarily point to wrongdoing. Our analysis begins by conducting a test on the variances of each level of the factor, as our future analysis relies on the equivalence of these variances. Using a two-sided F-test, we find a p-value greater than our pre-determined significance level of 0.05, and therefore fail to reject Ho and conclude that the variances are not significantly different. Knowing that the variances between factors are not significantly different, we proceed to the one-way ANOVA test, with the factor being the retirement facility tested, and the response variable being the charge for the service in units of USD ($). Our collected data exhibit a p-value greater than our pre-determined significance level (0.05)> 0.05. This therefore ends our analysis, and we ask the court to dismiss our case against DEFENDANT. Problem 3 Two junior attorneys named Jimmy and Kim have strong evidence that a retirement facility called Sandpiper Crossing has been systematically overcharging their residents. If their suspicions are true, the management at Sandpiper would be liable for tremendous fines and potentially even prison time. Unfortunately, their strongest evidence was obtained illegally by Jimmy and so it is inadmissible in court. Now, they are scram- bling to find other evidence to support their case. As part of their investigation, they conduct a randomized experiment by sampling the rates charged for a standard service at four different retirement facilities in the greater Albuquerque, NM area. The data collected are shown below in Figure 3. Sample Service charge number 1 ($) Retirement facility 207.56 Paloma Landing 202.96 Paloma Landing 2 3 202.19 Paloma Landing 4 201.16 Paloma Landing 5 6 7 8 9 10 11 12 13 14 15 16 17 202.36 Paloma Landing 207.51 Sandpiper Crossing 207.34 Sandpiper Crossing 206.95 Sandpiper Crossing 204.33 Sandpiper Crossing 207.99 Sandpiper Crossing 203.83 ABQ Grand Living 201.07 ABQ Grand Living 204.15 ABQ Grand Living 204.04 ABQ Grand Living 205.77 ABQ Grand Living 207.99 The Montebello 203.73 The Montebello 18 201.11 The Montebello 19 203.78 The Montebello 20 201.02 The Montebello Figure 3: Data collected for Problem 3. (a) (b) (20 points) Comment on Jimmy and Kim's experiment design. Is there anything that could be improved to help their case? 4 (50 points) Fill in the partial ANOVA table below and compute a p-value for the one-way ANOVA. What hypotheses are being tested, and what is the conclusion? source factor error SS DF MS F total 118.70 (c) (50 points) Differing in their approach to statistical analysis, Jimmy and Kim wrote separate reports with their own conclusions, shown in Appendix 1 and 2, respectively. Whose analysis do you agree with, and why? Make sure to justify your conclusions! (d) (25 points) What advice do you have for Jimmy and Kim at this point? Is there any way to salvage the case? Appendix 1 Analysis by James McGill, Esq. As part of ongoing litigation against Sandpiper Crossing, LLC (referred to hereafter as DEFENDANT), the law office of Wexler-McGill, representing the residents of Sandpiper Crossing (referred to hereafter as CLIENT) conducted an experiment to prove that DEFENDANT has knowingly, systematically, and maliciously overcharged CLIENT, with damages estimated in the millions of dollars. We compared estimates for the population mean charge for a standard service across four comparable retirement facilities across the greater Albuquerque, NM area. Our collected data, summarized in Figure 3, clearly illustrate the malice with which DEFENDANT overcharged CLIENT. To support our case, we conducted pairwise t-tests, which test for statistically significant differences in population means. The tests and our conclusions are shown below. Test 1: Ho PSP PABQGL H PSP PABQCL (1) (2) where sp refers to the population mean service charge at Sandpiper Crossing, and #ABQGL refers to the population mean service charge at ABQ Grand Living. In this test, we reject Ho with p-value = 0.04 < 0.05, and therefore conclude that the service charge at Sandpiper Crossing is significantly different than the charge for the same service at ABQ Grand Living. Test 2: Ho: H: PSP=PPL PSP PL (3) (4) where #sp refers to the population mean service charge at Sandpiper Crossing, and #PL refers to the population mean service charge at Paloma Landing. In this test, we reject Ho with p-value = 0.03 < 0.05, and therefore conclude that the service charge at Sandpiper Crossing is significantly different than the charge for the same service at Paloma Landing. Test 3: Ho: H: PSP=PM PSP #PM (5) (6) where sp refers to the population mean service charge at Sandpiper Crossing, and M refers to the popula- tion mean service charge at The Montebello Landing. In this test, we reject Ho with p-value = 0.02 < 0.05, and therefore conclude that the service charge at Sandpiper Crossing is significantly different than the charge for the same service at The Montebello. As the court can see, in all cases the service charge at Sandpiper Crossing is significantly different than the charge at a comparable retirement facility, and in fact the charge is systematically higher across all tests. This proves that DEFENDANT is guilty of systematically overcharging CLIENT, and we ask the court for the maximum damages allowed by law. Appendix 2 Analysis by Kimberly Wexler, Esq. As part of ongoing litigation against Sandpiper Crossing, LLC (referred to hereafter as DEFENDANT), the law office of Wexler-McGill, representing the residents of Sandpiper Crossing (referred to hereafter CLIENT) conducted an experiment to prove that DEFENDANT has knowingly, systematically, and maliciously overcharged CLIENT, with damages estimated in the millions of dollars. We compared estimates for the population mean charge for a standard service across four comparable retirement facilities across the greater Albuquerque, NM area. Our collected data, summarized in Figure 3, show that although the sample mean service charge is indeed higher at DEFENDANT's facility, they do not necessarily point to wrongdoing. Our analysis begins by conducting a test on the variances of each level of the factor, as our future analysis relies on the equivalence of these variances. Using a two-sided F-test, we find a p-value greater than our pre-determined significance level of 0.05, and therefore fail to reject Ho and conclude that the variances are not significantly different. Knowing that the variances between factors are not significantly different, we proceed to the one-way ANOVA test, with the factor being the retirement facility tested, and the response variable being the charge for the service in units of USD ($). Our collected data exhibit a p-value greater than our pre-determined significance level (0.05)> 0.05. This therefore ends our analysis, and we ask the court to dismiss our case against DEFENDANT. Problem 3 Two junior attorneys named Jimmy and Kim have strong evidence that a retirement facility called Sandpiper Crossing has been systematically overcharging their residents. If their suspicions are true, the management at Sandpiper would be liable for tremendous fines and potentially even prison time. Unfortunately, their strongest evidence was obtained illegally by Jimmy and so it is inadmissible in court. Now, they are scram- bling to find other evidence to support their case. As part of their investigation, they conduct a randomized experiment by sampling the rates charged for a standard service at four different retirement facilities in the greater Albuquerque, NM area. The data collected are shown below in Figure 3. Sample Service charge number 1 ($) Retirement facility 207.56 Paloma Landing 202.96 Paloma Landing 2 3 202.19 Paloma Landing 4 201.16 Paloma Landing 5 6 7 8 9 10 11 12 13 14 15 16 17 202.36 Paloma Landing 207.51 Sandpiper Crossing 207.34 Sandpiper Crossing 206.95 Sandpiper Crossing 204.33 Sandpiper Crossing 207.99 Sandpiper Crossing 203.83 ABQ Grand Living 201.07 ABQ Grand Living 204.15 ABQ Grand Living 204.04 ABQ Grand Living 205.77 ABQ Grand Living 207.99 The Montebello 203.73 The Montebello 18 201.11 The Montebello 19 203.78 The Montebello 20 201.02 The Montebello Figure 3: Data collected for Problem 3.