NAME: Math 403 Final Exam 12/10/08 15 questions, 150 points. You may use calculators and tables of z, t values on this exam.

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1 NAME: Math 403 Final Exam 12/10/08 15 questions, 150 points. You may use calculators and tables of z, t values on this exam. (10 pts) 1. Barry Bonds' home run totals for each year of his career ('86-'07): Make a histogram or stemplot to display this distribution. Discuss the general shape of the distribution and any interesting features. (10 pts) 2. On Monday, Cubs second baseman Ron Santo received hall of fame votes from 39 of the 64 veterans committee members. Was his total significantly different from the 75% needed to get into the hall of fame? Report the P-value with your answer.

2 (10 pts) 3. The Hannukah game of 'Dreidel' involves spinning a four sided top to win money from a 'pot'. All four sides are equally likely, and have the following meanings: Nun - nothing happens Gimel - the player takes the entire pot Hey - the player takes half of the pot Shin - the player loses one coin, and puts it in the pot With 8 coins in the pot, what is the expected number of coins won on the next spin? (10 pts) 4. Dissman and Han (2006) studied a tuning fork test for foot and ankle fractures. They used the test on 49 patients. The tuning fork test was positive for fractures on 22 of these patients. X-rays of all 49 patients determined that 5 actually had fractures, and all 5 were identified by the tuning fork test. a. What is the probability that a random subject from this experiment had a fracture and tested positive? b. What is the probability that a random subject from this experiment tested positive, given that they had no ankle fracture? (This is the sensitivity of the test).

3 (10 pts) 5. Dr. R. Davis, Jr. built a 100,000 gallon tank of liquid 'perc' about a mile underground in a coal mine to detect solar neutrino radiation (work for which he won the 2002 Nobel Prize in Physics). Neutrino detection in the tank is modeled by a Poisson process with an arrival rate of approximately λ = 0.5 netrinos/day. What is the probability that 7 days pass with no neutrino detected? (The PDF for the exponential distribution is f t = e t, t > 0) (10 pts) 6. CNN/Opinion Research wants to determine the percentage of Americans in favor of a federal bailout of the U.S. auto industry. How many people should they poll to get a margin of error of 2% with 95% confidence?

4 (10 pts) 7. More CO 2 may cause plants to grow faster. Using an elaborate apparatus, researchers are able to pipe extra CO 2 into a 30 meter wide circle of forest. They selected pairs of nearby circles in three parts of a pine forest, and randomly assigned one of each pair to receive extra CO 2. They then measured the mean increase in base area for trees in each circle over one growing season. Their data, for one year: Pair Control Plot Extra CO 2 Plot State and carry out a hypothesis test that the mean for the extra CO 2 plots is higher than the mean for the control plots. Report your conclusion using a significance level of α= (10 pts) 8. What are the main advantages and disadvantages of the (non-parametric) signs test versus the (parametric) one-sample t test?

5 (10 pts) 9. Eli Lilly and Co. has submitted the drug Olanzapine for FDA approval for the treatment of adolescent schizophrenia. The FDA will either accept or reject the drug for this use. Explain the two types of error the FDA can make, and for each, discuss who is harmed by the error. (10 pts) 10. For each of the five boldface numbers, decide if it is a parameter or a statistic. a. Using the 8 planets in our solar system, the regression line for planet density on planet diameter is given by y= x b. For St. Louis tap water in 2007, the maximum turbidity sampled was 0.11 NTU, significantly less than the water quality standard of 1.00 NTU. c. From , the S&P 500 has an average annual return of 9.2% with a standard deviation of 16%.

6 (10 pts) 11. Seals Unlimited manufactures extruded rubber seals in various sizes. Their precision class E2 seal comes in a 1 size that varies with a tolerance (standard deviation) of σ = From a large batch, they measure a random sample of 50 seals and find the sample mean is Give a 95% confidence interval for the measurement of the seals in the batch. (10 pts) 12. Continue with the rubber seals of the previous problem. State and carry out a hypothesis test that the mean size of the batch is 1. Give the P- value.

7 (10 pts) 13. For each plot, decide which of the three lines is the regression line of y on x and make your best guess for the correlation coefficient r: (10 pts) 14. The mean height of American women in their twenties is about 64 inches, and the standard deviation is about 2.7 inches. For men the same age, the mean is 69.3 with an SD of 2.8. The correlation between the heights of husbands and wives is r = 0.5. a. Find the equation of the regression line for the height of the wife as a function of the husband's height. b. What is the expected height the wife of a 70 tall man?

8 (10 pts) 15. Prove that the sum of the residuals for a least squares regression line is 0. That is, show i=1 e i =0 n

Chapter 12 Practice Test

Chapter 12 Practice Test 1. Which of the following is not one of the conditions that must be satisfied in order to perform inference about the slope of a least-squares regression line? (a) For each value