STA4809_2023_TL_011

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University of South Africa *

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4809

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Statistics

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Nov 24, 2024

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pdf

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Uploaded by ChancellorFang8501

Define tomorrow. university of south africa Tutorial letter 011/0/2023 Nonparametric Regression STA4809 Year module Department of Statistics ASSESSMENT 01 STA4809/011/0/2023

ASSESSMENT 01 Unique Nr.: 230204 Fixed closing date: 28 April 2023 QUESTION 1 A study is conducted comparing two competing medications for asthma. Sixteen subjects are involved in the investigation. The data shown reflect asthma symptom scores for patients randomly assigned to each treatment. Higher scores are indicative of worse asthma symptoms. (a) Test the null hypothesis that there is no difference in asthma symptoms between medications. Apply the Wilcoxon Signed-Ranks Test. Use α = 0 . 05 . Report your findings. For the test, provide the null and alternative hypotheses , critical region (or rejection region ), test statistics and your conclusions . (7) (b) Determine the p -value for the test that you have conducted in part (a). (3) (c) Conduct the Wilcoxon Rank Sum test using the normal approximation at a 5% level of signifi- cance. Report your findings. For the test, provide the null and alternative hypotheses , critical region (or rejection region ), test statistics and your conclusions . Which test, part (a) or part (c) do you recommend for the study? Why? Explain. (10) Table 1: Treatment A 55 60 80 65 72 78 68 71 Treatment B 23280 82 86 89 76 81 90 76 2

STA4809/011/0/2023 QUESTION 2 It is proposed that animals with a northerly distribution have shorter appendages than animals from a southerly distribution. Using the Mann-Whitney U procedure, test an appropriate hypothesis at a 5% level of significance for wing-length data for birds (data are in millimeters) given in Table 2. Table 2: Northern Southern 120 116 113 117 125 121 118 114 116 116 114 118 119 123 120 For the test, provide the null and alternative hypotheses , critical region (or rejection region ), test statistics and your conclusions . (10) 3

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QUESTION 3 A pharmaceutical company is interested in the effectiveness of a new preparation designed to relieve arthritis pain. Three variations of the compound have been prepared for investigation, which differ according to the proportion of the active ingredients: T15 contains 15% active ingredients, T40 contains 40% active ingredients, and T50 contains 50% active ingredients. A sample of 20 patients is selected to participate in a study comparing the three variations of the compound. A control compound, which is currently available over the counter, is also included in the investigation. Patients are randomly assigned to one of the four treatments (control, T15, T40, T50) and the time (in minutes) until pain relief is recorded on each subject. The data are presented in Table 3 below. Table 3: Control: 12 15 18 16 20 T15: 20 21 22 19 20 T40: 17 16 19 15 19 T50: 14 13 12 14 11 (a) Use the Kruskal-Wallis H -test to perform the test at a α = 0 . 05 level of significance that the four treatments are equally effective to relieve arthritis pain among patients. Report your findings. For the test, provide the null and alternative hypotheses , critical region (or rejection region ), test statistics and your conclusions . (10) (b) If the null hypothesis of part (a) above is rejected, then perform a pairwise comparisons using an appropriate method. (10) [50] 4