HP340: Statistical Methods, Spring 2015Due: 3:30 p.m., Tuesday April 14, 2015Homework 10Total Points: 50Show your work/explain your reasoning when calculations are required. Late assignments will notbe accepted.1. (33 points total) To examine the relationship between total cholesterol and systolic blood pressure researchers collected the following data from 20 subjects (data set in comma separated format: bp.csv):Subject Cholesterol (mg/dL) Blood pressure (mmHg)1 219 1702 203 1323 210 1294 208 1445 210 1456 177 1227 202 1248 225 1459 197 13710 180 11511 184 12712 220 14813 240 14814 224 14415 210 13316 239 15017 191 12018 175 11919 198 12520 200 131a. (5 points) Use JMP to construct a scatterplot of cholesterol and blood pressure and describe the relationship between the two variables. Cholesterol and Blood Pressure appear to have a linear relationship.b. (5 points) Compute the correlation coefficient by hand and check your result with JMP. (attached)c. (5 points) State the null hypothesis that cholesterol and blood pressure are not linearly related. State the alternative hypothesis. Perform the test at the 5% level. What conclusion do you reach about the relationship between cholesterol and blood pressure based on this sample?Null: Cholesterol and blood pressure are not correlated in the population.Alternative: Cholesterol and blood pressure are correlated in the population.H0: ρ=0H1: ρ≠0df=20-2=18  rcrit=0.444, robs=0.795|robs|>rcritWe reject the null hypothesis, accept the alternative.It is decided that cholesterol and blood pressure are correlated in the population from which the sample was selected.d. (3 points) Use JMP to plot histograms of both cholesterol and blood pressure to checkthe assumption of normality required for the test in part c. Does the test seem appropriate?Since there are few outliers, the Pearson hypothesis test seems appropriate based on the fact that outliers do not drastically affect Spearman’s test.e. (5 points) Based on the scatterplot in a., does there seem to be any outliers? If so, recomputed the Pearson correlation (using JMP) removing them and comment on anydifference with the correlation computed in b. Yes, there are some outliers.The correlation between blood pressure and cholesterol has increased to 0.878.f. (2 points) Compute the Spearman correlation by hand and check your result with JMP. (attached)g. (3 points) Which correlation coefficient is more appropriate to summarize the relationship between cholesterol and blood pressure in this dataset?The Pearson correlation coefficient is more appropriate to summarize the data since it measures a linear relationship.h. (5 points) Based on the analysis in a)-g)I. Can you use blood pressure to predict the cholesterol level of an individual?Yes, because the hypothesis test shows that they are correlated.II. What can you conclude based on your analysis in a-g about the causal relationship between cholesterol and blood pressure?Blood pressure and cholesterol are correlated but there is no evidence of causality between the two since correlation does not imply causation.2. (17 points total) In a music competition, participants were ranked (out of 10) by two judges (data set in comma separated format: judge.csv). Participant Judge 1 Judge 21 5 72 9 83 3 64 8 75 6 86 7 57 4 108 8 69 4 510 6 8a. (3 points) Plot the data using JMP.b. (6 points) Calculate the Pearson and Spearman correlation coefficients between the ranks of the two judges both by hand and using JMP. Comment on your findingsBy hand (attached), Pearson JMP above, spearman JMP below.There is minimum correlation between Judge 1 and judge 2 according to Spearman, and there is no correlation between the two judges based off Pearson.c. (5 points) Perform a 5% level test to of the null hypothesis that the population Spearman correlation coefficient is zero.H0: ρs=0H1: ρs≠0Npairs=10  rs-crit=0.648rs-obs=0.112|rs-obs|<rs-critWe do not reject the null hypothesis, and do not accept the alternative hypothesis.d. (3 points) What do you conclude about the agreement between the scores of the two judges?Based on Spearman, Pearson, and hypothesis tests, there is little to no correlation about the agreement between the scores of the two