STAT 201 Final, Fall 2003

on MERICAS I TVERSIT LIG@eary _~ American University of Beirut STAT 201 Elementary Statistics Fali 2003-2004 Final Exam Date: Friday. January 23. 2004 - 1:30 pm to 3:00 pm Instructor: Dr. Mohamed Kobeissi NA@M@s iccceececeeeeeeteeteeeeeeeeteeetttntetevteteeteeteneeee TD Fi evvttteeeeeee tee tteteteeeeeeeeteeecetenstteeeeseneneeee Section: 2 This is NOT an open-book exam. You are allowed to have a formula sheet and a calculator. There are 12 questions totaling 60 points. A question with more than one answer will be counted as wrong. A correct answer is 5 points, a wrong and/or an unanswered question is 0 points. Good Luck I. Use the following information to answer questions 1 to 3. Scores on an aptitude test are normally distributed with a mean of 220 and a standard deviation of 30. 1, For a random sample of size 50, what is the mean of the variable Z? > A. 220 B. 50 CG. 170 D. 30 E. none of the above nN . For a random sample of size 50, what is the standard deviation of the variable Z? A. 212.13 B. 50 C. 30 D. 4.24 E. none of the above “3. What is the probability that the sampling error made in estimating the population mean by the mean of a random sample of 50 test scores will be at most 5 points? A. 0.881 B. 0.135 C. 0.762 D. 0.999 E. none of the above 4. For the population of one town, the number of siblings is a random variable whose relative frequency histogram is left-skewed. Let £ denote the mean number of siblings for a random sample of size 45. For samples of size 45, which of the following statements concerning the sampling distribution of the mean is true? 1) Z 18 approximately normally distributed. ii) The distribution of @ is left-skewed. ili) The distribution of Z is approximately left-skewed. iv) ¥ is normally distributed. A. (i) B. Gi} C. (iii) D. iv} E. none of the above . Use the following information to answer question 5 to 7. A sample of 45 eggs yields a mean weight of 1.37 ounces. Assuming that o = 0.53 ounces. . Find the margin of error in estimating yz at the 95% confidence level. A. 0.15 B. 0.13 C. 6.71 D. 0.02 E. none of the above . Find a confidence interval for at the 95% confidence level. A. (0.37}2.37) B. [1.22;1.52) 9 C. (1.35:1.39]) 1D. {1.27:1.47! — E. none of the above . At 95% confidence level, what sample size is needed to ensure a margin of error of 0.1? A. 108 B. 86 C. 95 D. 241 E. none of the above . Suppose you have obtained a 95% confidence interval for u. Which of the following statements is/are true regarding the relationship between precision and confidence level? Assume the sample size is fixed. i) Decreasing the confidence level to 90% will result in a greater precision. ii) Increasing the confidence level to 99% will result in a narrower interval. iii) Increasing the precision will result in a higher confidence level. iv) Decreasing the precision will result in a higher confidence level. A. (ii) and (iil) B. (i) and (iv) C. {ii) and (iv) D. fi) and (iii) E. none . Suppose that (34.2;38.4) is a 99% z-distribution confidence interval for a population mean based on sample of size 50. What is the sample mean? A. 38.4 B. 72.6 C. 34.2 D. 36.3 FE. none of the above 10. Refer to previous question, what is the population standard deviation? = = A. 3.76 B. 7.57 C. 9.05 D. 3.9 E. none of the above 11. Suppose that scores for men on an aptitude test has greater standard deviation than scores for women on the same test. Based on a sample of size 50, a 95% confidence interval form the --~mean score, y, of all women has a margin of error of 2.2. Which of the following confidence intervals will have a smaller margin of error? i) A 95% confidence interval for the mean score of men. Sample size 30. ii) A 99% confidence interval for the mean score of women. Sample size 50. ili) A 95% confidence interval for the mean score of women. Sample size 100 A. (iii) B. (it) C. (i) D, fi) and (ii) and fiii) E. none of the above 12. Let X have a normal distribution with o = 1.1. What is the mean of X if P(X <7) =0.5. ALT B. 0.5 C. bl D. 7.8 E. none of the above 13. (bonus 2 points) STAT 201 was FUN? A. true B. false C. none of the above