A SAT prep course claims to increase student scores by more than 60 points, on average. To test this claim, 9 students who have previously taken the SAT are randomly chosen to take the prep course. Their SAT scores before and after completing the prep course are listed in the following table. Test the claim at the 0.01 level of significance. SAT Scores After Prep Course Difference Before Prep Course 1010 980 1170 1200 1040 1280 1450 1470 1500 1100 1260 1190 1280 1170 1370 1440 1500 1520 90 280 20 80 130 90 10 30 20 Ho:μd ≤60 Ha: μd > 60 ā-μd t = t = 83.33-60 84.56) .780 Test Statistic Critical Value: invT(.01, df: 9-1 = 8): 2.896 p-value: 0.2304 on Calculator 0.2304 0.01 Fail to Reject Conclusion: There is not sufficient evidence at the 0.01 level of significance to support the claim that students SAT scores increase by a mean of more than 60 points after completing the SAT prep courses. Gary has discovered a new painting tool to help him in his work. If he can prove to himself that the painting tool reduces the amount of time it takes to paint a room, he has decided to invest in a tool for each of his helpers as well. From records of recent painting jobs that he completed before he got the new tool, Gary collected data for a random sample of 6 medium-sized rooms. He determined that the mean amount of time that it took him to paint each room was 4.2 hours with a standard deviation of 0.5 hours. For a random sample of 4 medium-sized rooms that he painted using the new tool, he found that it took him a mean of 3.9 hours to paint each room with a standard deviation of 0.7 hours. At the 0.10 level, can Gary conclude that his mean time for painting a medium-sized room without using the tool was greater than his mean time when using the tool? Assume that the population variances are equal. (Pooled yes) Hay H₂ H₁₁> H2 (8₁-8₂)-(1-2) (4.2-3.9)-(0) -0.797 Test Statistic Critical Value: invT(.10, df: 5 - 1): 1.48 p-value: 0.224 on calculator 0.224 0.10 Fail to Reject Conclusion: There is not sufficient evidence to say that there is a reduction in Gary's mean time to paint a room using the new tool. A SAT prep course claims to increase student scores by more than 60 points, on average. To test this claim, 9 students who have previously taken the SAT are randomly chosen to take the prep course. Their SAT scores before and after completing the prep course are listed in the following table. Test the claim at the 0.01 level of significance. SAT Scores Before Prep Course 1010 980 1170 1200 1040 1280 1450 1470 1500 After Prep Course 1100 1260 1190 1280 1170 1370 1440 1500 1520 Difference Hiha 560 Hapa > 60 d-pa [=74) 90 280 20 80 130 90 10 30 20 83.33 ▪=,780 Test Statistic 5 of 9