[10] 2. You and your friends form an \"exercise pact\": the ten (n = 10} of you promise to all honestly record your total steps walked for a week, and then at the end of the week you all compete to see who can get the best time on a 400 m run. These data are shown in a scatterplot below: Y2 B1:B10 20000 40000 00000 30000 10000012II'1 140000 Xi A1 :A1 0 y-axis: lime to complete the 400 m run (in seconds) x-axis: number of steps accumulated in the previous week Some details from the analysis: R2: .8761 line of best t: y = -0.0016x + 282.3738 [2] {a} Oops. Your friend only remembered to write down the coefcient of determination. Calculate the correlation. [1] {b} According to the model, what is the expected improvement to 400 at run time from ta king 10000 additional steps during the week? [2] {c} One of your friends, clearly an amateur statistician (or a capable comedian) announces that they intend to walk 176, 484 steps before next week's race. What is this person trying to accomplish, and do you think they/ll succeed? Justify youranswer. {lad} An onlooker mentions they accumulated 50,000 steps last week. What would you expect their 400 m run time to be? I [1] (e) According to this model, what is the slowest possible run time for the 400 m track? [3] _(f) An additional friend (who happens to be annoyingly fit for no good reason) spends the whole week watching movies on the couch, misses the contest time, but drives to the contest venue late and asks to be allowed to run. You reluctantly agree, and your friend adds a data point of 900 steps, 90 second run time. You reluctantly add this point as the 11th value to your data set and re-calculate the coefficient of determination: it becomes R2 = 0.2513. Using this new sample data set, determine the appropriate test result for a null-hypothesis test on the population correlation coefficient, using a null hypothesis of HO: p = 0 and an alternative hypothesis of HA: p/ 0 and a significance threshold of a = 0.05. You might find it useful to know that P ( p.262