Question

You overhear a conversation between Mark and Anne in the gym. Mark is saying that he can bench press on average 200 pounds. Anne responds that on average she can bench press more. Mark then challenges her, saying "Show it!" Apparently, Anne keeps track of her data well, because she answers: "In the last n = 45 times, I pressed y = 205 with s2 = 24.5 pounds." She then suddenly turns around, looks at you, and says: "You are taking 36-226, why don't you do the math!" (a) Conduct the test at level a = 0.05. Include in your answer: your hypotheses, the rejection region, and your conclusion in context. Your friend Qiang comes in and admits to you that he could never press 200 pounds. In the last n = 36 times, he pressed y = 185 with s2 = 22 pounds. He asks you: maybe if we do a two-sided test instead of a one-sided test, the difference between my average and 200 would not be significant? (b) Give a conceptual explanation of whether a one-sided or a two-sided test would be more likely to give him a non-significant result? (c) You tell Qiang: "If you don't want the difference to be significant, you should just mention a different s2 to your friends." Determine what range of values Qiang can report so that in a two-sided test at level a = 0.10, the difference is not significant.

Answer 1

* we have given : n= sample size = 45. ✓ = sample mean = 205, ²= sample variance = 24.5 pounds. M= population mean = 200 pounds. 4 conduct the test at level x=o.os, * To Test ! Ho! NO 200 vs H,: M 7200 ti Test statistics : t = ( -4) <\

1 t= (2005-200) 545 5 24.5 16.7763 1 * 250.05 level of significance * * critical value = df = (hal) = 44 is talleref = to.os, 44 51 20153 (from Region X Acceptance table) Rejection - & Rejection Region eegion 015 2015

* Decision :- we reject Ho at (1-2)X100% level of significance if It's tollarda here It's tollardf we reject Ho. conclusion : There is sufficient evidence to conclude that population mean is not equal to 200 pounds_ H=200, n = 36 9 = 185, 5?=22 © To Test :-HoiH = 200 vs Hi + 200 Test stahisher : t = 15-M) Sn = (185-200) 536 522 552

t = 1 -19.1880 *) 2 =0.05 4 df = (n-1) = 35. * Corbical value = Ediziolf = to.05,35 = (+2.030 1 (from table) * Decision : we reject Ho at C1-d) x 100% level of significance If It's tale, df here it's tal 2. of * conclusion :- there is sufficient evidence conclude that (M €200) population mean to is not

equal to the 20o. *) If we use here one failed rest : - toidf= [ 116895] - (from table) (Also we reject Ho) - conceptual explanation of whether a one sided test would be more likely to or two sidled give him a non significant result *) result is non significant if test statistic value is less than critical value.

*) test statistic value is small when sample variance is large, f difference of sample should be small ¢ sample mean & population size small as well as a level should be increase (II.,00 5%) then it chances to be result is non significant. - Determine what range of values Giang can report so that in a two sided test at

level - 2=0.10, the difference is not significant Y test statistic should be less than critical value. For that sample mean gj should be close to population mean [ie 195,- -.198, 1943 *) sample size should be less than 30. sample variance should be more te 35 to 40 then it is possible é e difference is to not fail to significant. reject Ho