24. Kordell is running a science experiment to see if students in 12" grade can do more pushups than students in gut grade. He collects a random group of 25 9" graders and a random group of 25 12th graders and records the number of pushups that each student can do. The results for the two samples are shown below: 9 Grade Sample 12" Grade Sample x, = 13.1 and s, = 5.4 x, =16.6 and $2 =6.5 (a) Calculate X, -x, . Does this calculation support the idea that 12" graders can do more pushups than 9th graders? (b) Kordell used a computer to shuffle the 50 results in two groups of 25 and repeatedly calculated the difference x, - x, for the sample means of the shuffled groups. He does this 200 times with the results shown below. Simulated Value of x, -x, Based on the simulation results, is the difference observed in (a) statistically significant enough to conclude 12" grade students can do more pushups than 9" grade students? Explain