p-value: 06710. (On Calculator) 0.6710>0.05 Fail to reject. Conclusion: The evidence does not support the cost effectiveness of the direct mail campaign at the 0.005 level of significance (i.e. not sufficient evidence). Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 32 randomly selected people who train in groups, and finds that they run a mean of 49.0 miles per week. Assume that the population standard deviation from group runners is known to be 4.2 miles per week. She also interviews a random sample of 30 people who train on their own and finds that they run a mean of 47.2 miles per week. Assume that the population standard deviation for people who run by themselves is 4.8 miles per week. Test the claim at the 0.05 level of significance. Holy=H2 H₁₁₂ (81-83)-(1-2) (49-47.2)-(0) = 1.57 Test Statistic Critical Value: invT(.025, 29): ±2.04 p-value: 0.1225 on Calculator. 0.1225 >0.05 Fail to Reject Conclusion: There is not sufficient evidence at the 0.05 level of significance to say that there is a difference between the mean numbers of miles run each week by group runners and individual runners who are training for marathons. 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 wout using the toor was greater man is mean time when using 4 of 9 A direct mail appeal for contributions from a university's alumni and supporters is considered cost effective if more than 15% of the alumni and supporters provide monetary contributions. To determine if a direct mail appeal is cost effective, the fundraising director sends the direct mail brochures to a simple random sample of 250 people on the alumni and supporters mailing lists. He receives monetary contributions from 40 people. Does this evidence support the cost effectiveness of the direct mail appeal? Use a 0.05 level of significance. Hap 2.15 Hp<.15 40 P = B = .16 250 p-p z = z = p(1-p) n .16-.15 .15(1-15) 250 0.443 Test Statistic Critical Value: invNorm(.05): -1.645 p-value: 06710. (On Calculator) 0.6710>0.05 Fail to reject. Conclusion: The evidence does not support the cost effectiveness of the direct mail campaign at the 0.005 level of significance (i.e. not sufficient evidence).