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##### Business Research Methods Homework 4

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Question;Business;Research Methods{Homework 4;Fall 2014;4.1;(15 points) The National Collegiate Athletic Association (NCAA);requires Di-vision II athletes to get a combined score of at least 820 on the;Mathematics and Critical Reading sections of the SAT exam in order to compete;in their rst college year. In 2011, the combined scores of the millions of;college-bound seniors taking the SATs were approximately Normal with mean 1012;and standard deviation approxi-mately 213. What percentage of all college-bound;seniors had scores less than 820?;4.2 (20 points) The annual rate of return on stock indexes is very;roughly Normal. Since 1945, the Standard & Poor's 500 index has had a mean;yearly return of 12.5%, with a standard deviation of 17.8%. Take this Normal;distribution to be the distri-bution of yearly returns over a long period.;(a);In what range do the middle 95%;of all yearly returns lie?;(b);The market is;down for the year if the return on the index is less than zero. In what;proportion of years is the market down?;(c);In what proportion of years does;the index gain 25% or more?;4.3;(20 points) A;randomized comparative experiment studied the e ect of diet on blood pressure.;Researchers divided 54 healthy test subjects at random into two groups. One;group received a calcium supplement, and the other group received a placebo. At;the beginning of the study, the researchers measured many variables on the;subjects. The average seated systolic blood pressure of the 27 members of the;placebo group was reported to be x = 114:9 with a sample standard deviation;s = 9:3.;(a);Give a 95% con;dence interval for the mean blood pressure of the population from which the;subjects were recruited.;(b);The recipe you;used in part (a) requires an important assumption about the 27 members who;provided the data. What is this assumption?;4.4;(25 points) The weight of candy packs that come out of a package;machine has a Normal distribution with mean 2 pounds and standard deviation 0.1;pounds. Weights;1;of di erent packs are independent. Let us denote the total weight;of n packs coming;out;of the same machine by Sn.;(a);What is the;distribution of Sn?;(b);What is the;distribution of the sample mean xn = Sn=n?;(c);Suppose we have checked 100 independent samples out of the same;machine;and the sample mean x100 happens to be;2.01 pounds. What is the 95% con dence interval this sample mean has generated?;Does it contain the true mean 2 pounds?;(d) What;is the chance for the 95% con dence interval generated by x100 to cover the;true mean 2 pounds?;4.5 (20 points) Table 1 contains;the IQ test scores of 31 seventh-grade girls in a Midwest school district.;Table 1;Problem 4.5;114;100;104;89;102;91;114;114;103;105;108;130;120;132;111;128;118;119;86;72;111;103;74;112;107;103;98;96;112;112;93;(a) We expect the distribution of IQ scores to be close to Normal.;Make a his-togram of the distribution of these 31 scores. Does your plot show;outliers, clear skewness, or other non-Normal features? Find the sample mean;and sample standard deviation of these scores.;(b) Treat the 31 girls as an SRS of all middle-school girls in the;school district. Give a 95% con dence interval for the mean score in the;population.;(c) In fact, the scores are those of all seventh-grade girls in one of;the several schools in the district. Explain carefully why we cannot trust the;con dence interval from (b).

Paper#61663 | Written in 18-Jul-2015

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