Statistics 245 Homework Solutions: Sampling and Hypothesis Testing Problems, Assignments of Data Analysis & Statistical Methods

Download Statistics 245 Homework Solutions: Sampling and Hypothesis Testing Problems and more Assignments Data Analysis & Statistical Methods in PDF only on Docsity! Statistics 245 Homework #5 Solutions Problem #3.74 a) One possible population: all full-time undergraduate students in the fall term on a list provided by the registrar. b) A stratified sample with 125 students from each year is one possibility. c) Mailed questionnaires might have high nonresponse rates. Telephone interviews exclude those without phones, and may mean repeated calling for those that are not home. Face to face interview might be more costly than your funding will allow. Problem #3.75 a) Use a block design with blocks based upon race. Then randomly assign the one of two treatments (calcium, or placebo) to each of these blocks. Then observe changes in blood pressure b) A larger group gives more information- when more subjects are involved, the random differences between individuals have less influence, and we can expect the average of our sample to be a better representation of the whole population. Problem #5.4 a) The population is three times larger than the sample; it should be at least 10 times larger. b) np=(500)(0.002)=1 is too small; it should be at least 10. Problem #5.8 a) This is the probability that 26 to 34 people from the sample jog: P(26 £ X £ 141)=0.6273. Using normal approximation for Binomial, X: 0.5717, with Continuity correction, 0.6271. Using normal approximation for phat: 0.5704, with continuity correction: 0.6266 b) the normal approximations to the binomial X: for n=800: 0.8869, for n=1600: 0.9749, for n=3200: 0.9985. The normal approximations for phat for n=800: 0.8858, for n=1600:0.9750, for n=3200: 0.9984. Generally, we can conclude that as the sample size goes up, the probability that our estimate is accurate increases. Problem #5.12 If the university’s claim is true, X—the number of athletes in our sample who graduated—would have a binomial distribution with n=20 and p=0.80. a) P(X=11)=0.0074. b) P(X £ 11)=0.0100. Problem #5.18 a) £ =(300)(0.21)=63, £ 2=49.77 £ £ » 7.0548. b) np=63 and n(1-p)=237 are both more than 10. The normal approximation gives 0.0080, or 0.0097 with the continuity correction.