Independent- and Paired-Samples t-tests In the Tour de France, the world's best known bicycle race, some cyclists were expelled for attempting to enhance their performance by "blood doping\" with a synthetic hormone, erythropoietin or EPO, that stimulates the production of oxygen-bearing (and fatigue-inhibiting) red blood cells. Assume that a mental health investigator at a large clinic wants to determine whether EPOviewed as a potential therapeutic toolmight increase the endurance of severely depressed patients. For the independent-samples test. assume that volunteer patients are randomly assigned to one of two groups: A treatment group (X1) that receives a prescribed amount of EPO, and a control group (X2) that receives a harmless neutral substance. Subsequent endurance scores are based on the total time, in minutes, that each patient remains on a rapidly moving treadmill. What is the difference between these groups? Independent Samples Data: ID Score Group 1 12 1 2 5 1 3 11 1 4 11 1 5 9 1 6 18 1 7 7 2 8 3 2 9 4 2 10 6 2 11 3 2 12 13 2 For the paired-samples test, assume that the endurance scores of patients not only reflect any effects of EPO (if any exist) but also random effects of many uncontrolled factors that may be particular to the individual patients (e.g., their athleticism). Therefore, in this experiment, each patient is measured twiceonce under the treatment condition (X1) and once under a controlled condition (X2). Determine if there is a difference between these two experiences. Paired Samples Data: ID Doped Not doped 1 12 7 2 5 3 3 11 4 4 11 6 5 9 3 6 18 13 For both the Independent- and Paired-Samples t-Tests: 1. Specify the null and research/alternative hypotheses. 2. Set a = .05 and state the value of tc. 3. Calculate the t statistic by hand, showing all work. 4. Verify your answer and null hypothesis decision with the Jamovi output. 5. Based on the output, explain whether the t-test assumption(s) were met. 6. State the outcome in APA style (i.e., identify the specific statistical test, state the research/alternative hypothesis in words, describe the pattern of results in words, support your written results with Ms, SDs, t, df, p-value, and Cohen's d).Descriptives N Mean Median SD SE 6 11.0 4.2 1.7 Doped 11.00 0 3 Not 6 6.00 3.7 Doped 5.00 .5 9 Plots Doped - Not Doped 12.5 10.0 - o Mean (95% CI) 7.5 o Median 5.0 2.5 Doped Not Doped Standardized Residuals 0