Name: MIDTERM TWO QUESTION 1 (40 pts): HAND CALCULATIONS You may use SPSS or other tools to check your hand calculations. The dataset DualHIVInfection. sav contains information on 38 HIV-infected individuals enrolled in a neurocognitive multi-center observational study in the US. The variables you will use for this question are as follows: Age = participant's age, in years CD4 = participant's current CD4 T-cell count in cells/mm3 Conduct a hypothesis test (at alpha=0.01 and alpha=0.005 levels) to understand the relationship (correlation) between the study participants' CD4 T-cell count and their Age. The scatter plot (left) of CD4 T cell count to Age and the histogram (right) of CD4 T- Cell Count are provided. Pearson Correlation Coefficient = 0.254. Spearman Correlation Coefficient = 0.429. CD (a) (6 pts) What is the null and alternate hypotheses? Ho: HA: (b) (10 pts) Using the Pearson correlation coefficient, compute the test statistic. Show the computation steps for full credit.(c) (10 pts) Using the Spearman correlation coefficient, compute the test statistic. Show the computation steps for full credit. (d) (8 pts) Fill in the following table: PEARSON SPEARMAN Critical Value Conclusion about Ho Conclusion about Ho (2 decimal places) Circle the correct answer Circle the correct answer Alpha = 0.01 Reject Fail to Reject Reject Fail to Reject Alpha = 0.005 Reject Fail to Reject Reject Fail to Reject (e) (1 pts) For this problem, do Pearson and Spearman correlation give consistent results in terms of the association of CD4 and Age? CIRCLE the correct answer: YES NO (f) (5 pts) Which correlation coefficient should be used for this study and why (include a discussion of the test assumptions in the answer)