PHC 5052 BiOStatiStiCS HW#4 Due 4/11/2022 -._'I' 0.1. A camera has been developed to detect the presence of cataract more accurately. Using this camera, the gray level of each point (or pixel) in the lens of a human eye can be characterized into 256 gradations, where a gray level of 1 represents black and a gray level of 256 represents white. To test the camera, photographs were taken of 6 randomly selected normal eyes and 6 randomly selected cataractous eyes (the two groups consist of different people). The median gray level of each eye was computed over the 10,000+ pixels in the lens. The data are given in HW4 C11.sav on Blackboard. 1) What statistical procedure can be used to test whether there is a signicant difference in the median gray levels between cataractous and normal eyes? Explain why using the appropriate graphs. 2) Carry out the test procedure mentioned in part 1). Use a: 0.10, and both rejection region and p-value to make a decision. 3) Provide a 9096 C! for the mean difference in median gray levels between cataractous and normal eyes. Interpret the condence interval. 0.2. An important hypothesis in hypertension research is that sodium restriction may lower blood pressure. However, it is difficult to achieve sodium restriction over the long term, and dietary counseling in a group setting is sometimes used to achieve this goal. The data on urinary sodium in HW4 Q2.sav on Canvas were obtained on 8 individuals enrolled in a sodium- restricted group. Data were collected at baseline and after 1 week of dietary counseling. Assume the population of urinary sodium is following a normal distribution. 1) What are appropriate hypotheses to test whether dietary counseling is effective in reducing sodium intake over a 1-week period (as measured by overnight urinary sodium excretion)? Explain why. 2) Carry out the test procedure mentioned in part 1). Use a: 0.05, and both rejection region and p-value to make a decision. 3) Provide a 95% Ci for the true mean change in overnight sodium excretion over a 1-week period. Interpret the condence interval. (13. We' re interested in whether angrier people tend to get heart disease more often. Here is the complete table of observed counts for the CHD and anger level side by side. Do the data below provide convincing evidence of an association between anger level and heart disease in the population of interest? Low anger Moderate anger High anger Total CRD 60 100 40 200 No CH!) 3000 4500 560 8060 Total 3060 4600 600 8260 1) Use a = 0.05 and rejection region to make a decision (calculate by hand). 2] Create dataset in SPSS and solve part 1). C14. A physician claims that a person's diastolic blood pressure can be lowered, if, instead of taking a drug, the person listens to a relaxation tape each evening. Ten subjects are randomly selected. Their blood pressures, measured in millimeters of mercury, are listed below. The 10 patients are given the tapes and told to listen to them each evening for one month. At the end of the month. their blood pressures are taken again. The data are listed below. 1 2 3 4 5 6 7 8 9 10 Before 86978396959080999389 After .918388898783898973 Which of the following ve test procedures is best to test the physician's claim? Explaln why. A. Two sample t-test, B. Paired t-test, C. Sign test, D. Wilcoxon signed rank test, E. Wilcoxon rank sum test. *HW4 Q1.sav [DataSet1] - IBM SPSS Statistics Data Editor File Edit View Data Transform Analyze Graphs Utilities Extensions Window H TT TT H Pat Grey_level da Group ient var var var va ID 1 161 Catal 140 Catal 136 Catal 171 Catal 106 Catal 149 Catal 158 Normal 182 Normal LO 9 185 Normal 10 10 145 Normal 11 11 167 Normal 12 12 177 Normal 13 1HW4 Q2.sav [DataSet1] - IBM SPSS Statistics Data Editor ile Edit View Data Transform Analyze Graphs Utilities Extensions Window Help TTTT H A Person Week0 Week1 Difference var var var var var 7.85 9.59 -1.74 12.03 34.50 -22.47 21.84 4.55 17.29 13.94 20.78 -6.84 16.68 11.69 4.99 41.78 32.51 9.27 14.97 5.46 9.51 CO 12.07 12.95 -.88 LO 10 11 12 13