Midterm1PracticeShortAnswer：1个简短的回答中的实践(可编辑).doc

Midterm 1 I Practice -ShortAnswer: 1个简短的回答中的实 践（可编辑）（文档可以直接使用，也可根据实际需要修改使用 ，可编辑推荐下载）Practice Questi ons for Exam 11. The height of male stude nts at your college/u ni versity is no rmally distributed with a mean of 70 in ches and a sta ndard deviati on of 3.5 in ches. If you had a list of teleph one n umbers for male stude nts for the purpose of con duct ing a survey, what would be the probability of ran domly call ing one of these stude nts whose height is:⑻ taller than 6'0"?(b) between 5'3" and 6'5"?(c) shorter tha n 5'7", the mean height of female stude nts?(d) shorter than 5'0"?(e) taller than Shaquille O'Neal, the cen ter of the Bost on Celtics, who is 7'1" tall?Compare this to the probability of a woma n being preg nant for 10 mon ths (300 days), where days of pregnancy is normally distributed with a mean of 266 days and a standard deviation of 16 days.An swer:(a) Pr(Z > 0.5714) = 0.2839;(b) Pr( — < Z < 2) = 0.9545 or approximately 0.95;(c) Pr(Z < -0.8571) = 0.1957;>2.99 =(d) Pr(Z < -2.8571) = 0.0021;(e) Pr(Z > 4.2857) = 0.000009 (the text does not show values above 2.99 standard deviations, Pr(Z 0.0014) and Pr(Z > 2.1250) = 0.0168.2) Adult males are taller, on average, than adult females. Visiting two recent American Youth Soccer Organi zati on (AYSO) un der 12 year old (U12) soccer matches on a Saturday, you do not observe an obvious differe nee in the height of boys and girls of that age. You suggest to your little sister that she collect data on height and gen der of childre n in 4 th to 6th grade as part of her scie nee project. The accompa nying table shows her findin gs.Height of You ng Boys and Girls, Grades 4 -6, in in chesBoysGirls召够!i| SGids57.83.95558.44.257(a) Let your n ull hypothesis be that there is no differe nee in the height of females and males at this age level. Specify the alter native hypothesis.(b) Find the differe nee in height and the sta ndard error of the differe nee.(c) Gen erate a 95% con fide nee in terval for the differe nee in height.(d) Calculate the t-statistic for comparing the two means. Is the differenee statistically significant at the 1%level? Which critical value did you use? Why would this n umber be smaller if you had assumed a one sided alter native hypothesis? What is the in tuiti on beh ind this?An swer:(a) H0 :也门护-叱袱=0 vs. H 1 :戸羯戸-叱漁 工0I — 2— I 77 — T ! 3.9 4.2 (b) 、晒-Y©晟=-0.6, SE(> 碍忻-、G泳)== °.77.(c) -0.6 ±1.96 X0.77 = (-2.11, 0.91).(d) t = -0.78, so t < 2.58, which is the critical value at the 1% level. Hence you cannot reject the nullhypothesis. The critical value for the one -sided hypothesis would have bee n 2.33. Assum ing a one -sidedhypothesis implies that you have some in formati on about the problem at hand, and, as a result, can be more easily convinced than if you had no prior expectation.3) Assume that two preside ntial can didates, call them Bush and Gore, receive 50% of the votes in thepopulati on. You can model this situati on as a Ber noulli trial, whereY is a ran dom variable with successprobability Pr( Y = 1) = p, and where Y = 1 if a pers on votes for Bush and Y = 0 otherwise. Furthermore, let? be the fracti on of successes (1s) in a sample, which is distributedp 1 pN (p, ) in reas on ably largensamples, say for n >40.(a) Given your knowledge about the population, find the probability that in a random sample of 40, Bush would receive a share of 40% or less.(b) How would this situation change with a random sample of 100?(c) Give n your an swers in (a) and (b), would you be comfortable to predict what the voti ng inten ti ons forthe entire population are if you did not know p but had polled 10,000 individuals at random andcalculated ? ? Expla in.(d) This result seems to hold whether you poll 10,000 people at random in the Netherlands or the UnitedStates, where the former has a population of less than 20 million people, while the United States is 15times as populous. Why does the population size not come into play?An swer:0.40 0.50⑻ Pr( p < 0.40) = Pr(Z < ==—) = Pr(Z < -1.26) ~0.104. In roughly every 10 th sample of this size,摩\ 40Bush would receive a vote of less tha n 40%, although in truth, his share is 50%.c 0.40 0.50O.25 I 100(b) Pr( ? < 0.40) = Pr(Z < ) = Pr(Z < -2.00) ~0.023. With this sample size, you would expect thisto happe n only every 50 th sample.(c) The an swers in (a) and (b) suggest that for eve n moderate in creases in the sample size, the estimator does not vary too much from the population mean. Polling 10,000 individuals, the probability of finding a? of 0.48, for example, would be 0.00003. Un less the electio n was extremely close, which the 2000 electi onwas, polls are quite accurate eve n for sample sizes of 2,500.(d) The distribution of sample means shrinks very quickly depending on the sample size, not the population size. Although at fi。