Assignment Stats 250 W11 HW 3 with answers

Assignment Stats 250 W11 HW 3 with answers - 4/17/2011

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Assignment Stats 250 W11 HW 3 Graded Point Total: 20 out of 30 1.5 out of 1.5 points a. 0.5 out of 0.5 points The sample proportion is _____ Your Answer: = 50/200 = .25 Solution: 50/200 = 0.25 Required Assignment Stats 250 W11 HW 3 Question 1 (Chapter 9) Consider the population of all UM undergraduate upper-class students. Suppose 20% of all such students have withdrawn from a class after the drop/add period ended. A random sample of n = 100 such students will be selected and the sample proportion that have withdrawn from a class after the drop/add period will be computed. What is the approximate distribution that describes the possible values for the sample proportion ? Give all aspects of the distribution. Your Answer: n*p = 100*.2 = 20 n(1-p) = 100*.8 = 80 Because n is large, and np>=10 and n(1-p)>=10, we would use the large sample normal approximation for computing the probability. The approximate normal distribution would be: N(po, sqrt((po(1-po))/n)) = N(.2, sqrt((.2*.8)/100)) = N(.2, .04) Solution: The distribution of the possible sample proportion ( ) values will be approximately normal with a mean of p =0.20 and a standard deviation of sqrt((.20(1-0.20))/100) = sqrt(0.0016) = 0.04. Using the notation for a normal distribution we have: N(0.20, 0.04). Question 2 (Chapter 9) In a random sample of n = 200 drivers, 50 individuals say that they never wear a seatbelt when driving. 4/17/2011 www.lecturebook.com/homeworks/sho… lecturebook.com/homeworks/show/37 1/12
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b. 0.5 out of 0.5 points The standard error of is _____ Your Answer: =Sqrt(( (1- ))/n) =Sqrt((.25*.75)/200)=.0306 Solution: sqrt((0.25*0.75)/200) = 0.03062 c. 0.5 out of 0.5 points In a different survey of n = 400 drivers, 100 people say they never wear a seatbelt when driving. The sample proportion is still _____ Your Answer: 100/400 = .25 Solution: 100/400 = 0.25 d. 0.5 out of 0.5 points ...but the standard error of is _____ Your Answer: =Sqrt(( (1- ))/n) =Sqrt((.25*.75)/400)=.0217 Solution: sqrt((0.25*0.75)/400) = 0.02165 e. 0.5 out of 0.5 points Summarize the differences from parts (a) and (b) to parts (c) and (d) regarding sampling for a survey. Your Answer: 4/17/2011 www.lecturebook.com/homeworks/sho… lecturebook.com/homeworks/show/37 2/12
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The main difference is the sample size: With the same sample proportion , the larger the sample size, the smaller the standard error. Solution: As the sample size goes up, the standard error of goes down. Thus,the estimator becomes more precise. 0.5 out of 0.5 points 1.5 out of 1.5 points Question 3 (Chapter 10) Estimating a Population Proportion. Suppose two researchers want to estimate the proportion of American college students who favor abolishing the penny using a conservative confidence interval. They both want to have about the same margin of error to estimate this proportion. However, Researcher 1 wants to estimate with 99% confidence and Researcher 2 wants to
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Assignment Stats 250 W11 HW 3 with answers - 4/17/2011

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