The accompanying data were read from a plot (and are a subset of the complete data set) given in an article. The data represent the mean response times for a group of individuals with closed-head injury (CHI) and a matched control group without head injury on 10 different tasks. Each observation was based on a different study, and used different subjects, so it is reasonable to assume that the observations are independent. Mean Response Time Study Control CHI 1 250 302 2 360 490 3 475 658 4 525 684 5 610 922 6 740 1044 7 880 1421 8 920 1329 9 10 1010 1200 1481 1815 (a) Fit a linear regression model that would allow you to predict the mean response time for those suffering a closed-head injury from the mean response time on the same task for individuals with no head injury. (Round your answers to three decimal places.) y = + X (b) Do the sample data support the hypothesis that there is a useful linear relationship between the mean response time for individuals with no head injury and the mean response time for individuals with CHI? Test the appropriate hypotheses using α = 0.05. Calculate the test statistic. (Round your answer to two decimal places.) t = What is the P-value for this test? (Use a statistical computer package to calculate the P-value. Round your answer to three decimal places.) P-value = What can you conclude? Do not reject Ho. We have convincing evidence of a useful linear relationship between mean response time for people with no head injury and mean response time for people with a closed-head injury. Reject Ho. We have convincing evidence of a useful linear relationship between mean response time for people with no head injury and mean response time for people with a closed-head injury. Reject Ho. We do not have convincing evidence of a useful linear relationship between mean response time for people with no head injury and mean response time for people with a closed-head injury. Do not reject Hò. We do not have convincing evidence of a useful linear relationship between mean response time for people with no head injury and mean response time for people with a closed-head injury. (c) It is also possible to test hypotheses about the y intercept in a linear regression model. For these data, the null hypothesis Ho: a = 0 cannot be rejected at the 0.05 significance level, suggesting that a model with a y intercept of 0 might be an appropriate model. Fitting such a model results in an estimated regression equation of CHI = 1.48(Control). Interpret the estimated slope of 1.48. For any given task, people with no head injury are predicted to have a reaction time that is 1.48 times as great as the reaction time for people with a closed-head injury. For any given task, people with no head injury are predicted to have an average reaction time that is 1.48 times as great as the average reaction time for people with a closed- head injury. For any given task, people with a closed-head injury are predicted to have an average reaction time that is 1.48 times as great as the average reaction time for people with no head injury. For any given task, people with a closed-head injury are predicted to have a reaction time that is 1.48 times as great as the reaction time for people with no head injury.