Final Exam Questions for Introduction to Statistical Analysis | ECON 160, Exams of Statistics

Download Final Exam Questions for Introduction to Statistical Analysis | ECON 160 and more Exams Statistics in PDF only on Docsity! Econ 160 Myles J. Callan Fall 2006 Final: Econ 160 – Introduction to Statistical Analysis Name:_______________________________________________________________________ Note: Please use the spaces provided for your answer, and give complete, detailed answers to each question. Good Luck! Question One: (60 points – 60 minutes) In a diagnostic study of anemia in the fetuses of pregnant women, the velocity of blood in a particular blood vessel in the fetus's head was measured using an ultrasound machine. In the following plot, the logarithm to base 10 of blood velocity (Y) is plotted against the gestational age in weeks (X) (taking logarithms on the Y scale was found to improve the statistical properties of the plot): Y is the log of blood velocity and X is the gestational age, measured in weeks. For these data points: The correlation r of X and Y is 0.911, the mean of the Y values, Y , is 1.581, the standard deviation of the Y values, Ys , is 0.1675, the mean of the X values, X , is 28.31, and the standard deviation of the X values, Xs , is 6.894. a) (10pts) Estimate, and interpret, the regression line in the form: Y = b + m X Page 2 of 14 b) (10pts) If the standard error for your estimate of the slope coefficient (m) is 0.00526, is the relationship between blood velocity and weeks of pregnancy “significant” ? Answer this question by first stating what null hypothesis you use to test if the relationship is significant, then derive the test statistic. Page 5 of 14 f) (4pts) Suppose we continue this straight line through to 11/01/2008, i.e. immediately before the next presidential election – this corresponds to X = 7:139 years (since 9/11/2001). What would be his predicted popularity on this date? g) (8pts) Is your answer to part (f) a realistic estimate? Briefly state why or why not. (Your answer should refer to the nature of the “experiment” – that is, the type of relationship that exists between X and Y) Page 6 of 14 h) (4pts) Some statisticians might argue that because the polls immediately around the time of the Iraq war (the ones marked `X' in the diagram) were clearly different from the rest, they should be excluded from any calculation of long-term trend. If we do exclude those polls, what do you think happens to the correlation coefficient r? Does it become (i) - 0.9304, (ii) -0.8716, (iii) - 0.6061, (iv) +0.9597 ? Circle which of those you think is correct, and briefly explain (There is no need for any calculation on this part.) Page 7 of 14 Question Two: (15 points – 15 minutes) The manager of a certain small restaurant has observed that the most popular entree is the fish entree. 30% of the diners select the fish entree. a) (1pts) Find the expected number of fish entrees ordered by a party of 4 diners. b) (2pts) Find the probability that in a party of 4 diners, exactly 2 of them order the fish entree. At a certain casino in Las Vegas, the slot machines require a $1 stake. The possible prizes are $5, $10, $20 and a jackpot of $100. According to the casino management, the probabilities of these prizes are respectively 0.1, 0.03, 0.005 and 0.0005. In all other cases, there is no prize. c) (2pts) If the above quoted probabilities are accurate, what is the expected payout for each $1 staked? Page 10 of 14 Question Three: (25 points – 25 minutes) It is commonly believed that blood pressure readings taken by a physician tend to be higher than those taken by a nurse (because people are more nervous in the presence of the physician). This is referred to as the ‘white coat’ effect. The data below are two readings (one by a physician and the other by a nurse) taken during the physical exam from 12 male participants in the Cardiovascular Health Study. Subject RN BP MD BP 1 120 125 2 124 126 3 130 138 4 118 117 5 140 143 6 128 128 7 140 146 8 135 133 9 126 127 10 130 135 11 126 126 12 127 131 Average 128.7 131.3 SD 6.9 8.2 Correlation 0.93 Where “RN” is registered Nurse, and “MD” is Doctor. Use hypothesis testing methods to assess whether, based on these 12 participants, there is a ‘white coat’ effect on systolic blood pressure. That is, statistically, is there a difference between the two sets of results. a) (2pts) State the null hypothesis. Remember that the hypothesis should be written in terms of the population parameters. b) (2pts) What test statistic will you use to test the hypotheses in a)? (Don’t compute it, just indicate what test statistic you will use.) Page 11 of 14 c) (10pts) Use the appropriate statistical procedure in to perform the calculations required for a hypothesis test at the 5% significance level. d) (3pts) What is the p-value for the test statistic? Page 12 of 14 e) (3pts) Would you conclude there is or is not a ‘white coat’ effect? Explain. f) (5pts) Calculate a 95% confidence interval of the mean blood pressure difference.