4. [I3 Points] DETAILS DEVORESTAT9 9.4.0545. MY NOTES I ' ASK YOUR TEACHER I ' PRACTICE ANOTHER Teen Court is a juvenile diversion program designed to circumvent the formal processing of rst-time juvenile offenders within the juvenile justice system. An article reported on a study in which offenders were randomly assigned either to Teen Court or to the traditional Department of Juvenile Services method of processing. Of the 56 Teen Court individuals, 17 subsequently recidivated during the 18-month follow-up period, whereas 14 of the 54 Department of Juvenile Services individuals did so. Does the data suggest that the true proportion of Teen Court individuals who recidivate during the specied follow-up period differs from the proportion of Department of Juvenile Services individuals who do so? Test the relevant hypotheses using a signicance level of 0.10. (Use p1 for the true proportion of Teen Court individuals who recidivate during the follow up period and p2 for the true proportion of individuals from the traditional Department of Juvenile Services who recidivate during the follow up period.) USE S State the relevant hypotheses. O Ho: p1 p2 0 Ha: p1 p2 = 0 O Ho: p1 p2 = 0 Ha: p1 p2 0 O Ho: p1 p2 = 0 Ha: 141 [42 > 0 OH:p1p2=0 Ha: p1 - p2 o Compute the value of the sample correlation coefficient, r. (Round your answer to four decimal places.) r = Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. Fail to reject Ho. A positive correlation exists between maximum lactate level and muscular endurance. O Fail to reject Ho. A positive correlation does not exist between maximum lactate level and muscular endurance. O Reject Ho. A positive correlation does not exist between maximum lactate level and muscular endurance. O Reject Ho. A positive correlation exists between maximum lactate level and muscular endurance. (b) If a regression analysis were to be carried out to predict endurance from lactate level, what proportion of observed variation in endurance could be attributed to the approximate linear relationship? Answer the question without doing any regression calculations. (Round your answer to four decimal places.) If a regression analysis were to be carried out to predict lactate level from endurance, what proportion of observed variation in endurance could be attributed to the approximate linear relationship? Answer the question without doing any regression calculations. (Round your answer to four decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question.14. [-/3 Points] DETAILS DEVORESTAT9 12.5.064. MY NOTES ASK YOUR TEACHER The accompanying data on x = UV transparency index and y = maximum prevalence of infection was read from a graph in an article. 1.2 1.4 1.5 2.0 2.1 2.7 2.7 2.7 2.8 2.9 3.0 3.5 3.8 3.8 4.5 5.1 5.7 15 3 31 1 13 0 8 15 2 1 7 35 25 10 35 58 56 Summary quantities include Sxx = 25.6506, Syy = 5546.2353, and Sxy = 265.1882. (a) Calculate the value of the sample correlation coefficient. (Round your answer to three decimal places.) Interpret the value of the sample correlation coefficient. O This indicates a moderate, positive association between UV transparency index and maximum prevalence of infection. O This indicates a weak, positive association between UV transparency index and maximum prevalence of infection. This indicates a weak, negative association between UV transparency index and maximum prevalence of infection. This indicates a moderate, negative association between UV transparency index and maximum prevalence of infection. (b) If you decided to fit the simple linear regression model to this data, what proportion of observed variation in maximum prevalence could be explained by the model relationship? (Round your answer to three decimal places.) (c) If you decided to regress UV transparency index on maximum prevalence (i.e., interchange the roles of x and y), what proportion of observed variation could be attributed to the model relationship? (Round your answer to three decimal places.) (d) Carry out a test of Ho: p = 0.5 versus Ha: p > 0.5 using a significance level of 0.05. [Note: The article reported the P-value for testing H: p = 0 versus Ho: p # 0.] (Round your test statistic to two decimal places and your P-value to four decimal places.) = P-value State the conclusion in the problem context. O Reject Ho. We do not have sufficient evidence to conclude that the population correlation coefficient for these two variables exceeds 0.5. O Fail to reject Ho. We have sufficient evidence to conclude that the population correlation coefficient for these two variables exceeds 0.5. O Reject Ho. We have sufficient evidence to conclude that the population correlation coefficient for these two variables exceeds 0.5. O Fail to reject Ho. We do not have sufficient evidence to conclude that the population correlation coefficient for these two variables exceeds 0.5. You may need to use the appropriate table in the Appendix of Tables to answer this