Stat 2411 Spring 2006 Final Exam (150 points total) Name _________________________________________________ (1) (8 points) Tell when to reject H0: - = 0 using a t-test. Answers would be of the form reject H0 when t < -2.479 reject H0 when |t| > 2.479 (t < -2.479 or t > 2.479) reject H0 when t > 2.479 State what df and what tabled probability level you used. (a) HA: - ≠, = 0.05, n1=10, n2=8 (b) HA: - < = 0.10, n1=10, n2=8 (c) HA: - > = 0.01 , n1=10, n2=8 (2) (8 points) Give the p-value (as near as you can tell from the table) for testing H0: = 0 using the t test given above for the following situations. After finding the p-value in each case, tell whether to reject or not reject H0 at the 0.05 level. (a) HA: - ≠ , n1=10, n2=8, t = -1.85 (b) HA: - ≠ , n1=10, n2=8, t = 0.43 (c) HA: - < , n1=10, n2=8, t = -3.05 (3) (10 points) A botanist is planning to plant lupine seeds of a particular variety to determine what proportion of the seeds yield plants with purple flowers. How many seeds must the botanist plant to be 95% confident of estimating the proportion of purple flowers with an error of no more than ± 0.01? (4) (15 points) The expected number of dinoflagellates in a cubic meter of uniformly mixed water is 0.5 dinos/m3. (a) What is the probability of finding 2 or more dinoflagellates in a random cubic meter of water? (b) What volume of water must be checked in order to have a 95% chance of finding at least 1 dinofalgellate? (5) (30 points) The results given below are for Clinical Global Impression scores for unmedicated and medicated patients. Clinical Global Impression Scores Unmedicated Patients Medicated Patients X 1 4.2 S1 1.0 n1 12 X 2 4.6 S 2 0.9 n2 10 (a) Find a 99% confidence interval for - . (b) Fill in the two blanks. On the basis of this confidence interval we would ____________ (reject or not reject) H0: - = 0 versus HA: - ≠ at the = ___________ level. (continued from previous page) (c) What do you have to assume for your statistical analysis to be valid? (d) How would you check to see if these assumptions are warranted? Tell explicitly what you would look for in deciding if the assumptions are met. (6) (25 points) A study comparing the effects of splints and surgery on treatment of carpal tunnel syndrome was reported in the September 11, 2002, issue of the Journal of the American Medical Association. The scientists found that 62 of 78 patients randomly assigned to surgery improved whereas only 46 of 86 patients wearing splints improved. Test the null hypothesis that the probabilities of improvement are the same for the two treatments against the alternative that the two treatments have different probabilities of improvement. Test at the = 0.01 level. (7) (5 points) A class has 15 boys and 20 girls. There are 3 left handed boys and 2 left handed girls. A child is picked at random from the class. Define the events B = a boy is chosen L = a left handed student is chosen Are the events B and L independent? Give appropriate numerical values to explain clearly why or why not. (8) (25 points) The following data are partial data from a study examining the efficacy of saliva cotinine as an indicator of exposure to tobacco smoke. (You may have seen signs around campus asking for subjects for such smoking research.) Four smokers who have abstained from smoking for at least one week then smoked a single cigarette. For each subject samples of saliva were taken 12 and 24 hours after smoking. Cotinine levels are given below. Subject 1 2 3 4 12 hr 73 58 67 93 24 hr 24 27 49 59 Test the null hypothesis that there is no difference in 12 and 24 hour cotinine levels versus the alternative hypothesis that the 12 hr and 24 hr levels are not the same. Use = 0.05. (9) (16 points) A population of plants has types dd, Dd and DD. The DD and Dd plants are tall; the dd plants are dwarf. There are 25% dd, 50% Dd and 25% DD plants. Type dd Dd DD Height dwarf tall tall Percent 25% 50% 25% (a) If a plant is picked at random, what is P(DD | tall)? (b) If 5 plants are picked at random, what is the probability of exactly 2 dwarf plants? (10) (8 points) (a) Give a definition of a p-value for a biology student who has not taken statistics. (b) In the paper Olfactory Impairment in Older Adults the authors found that 38% of the subjects with a manufacturing occupation had olfactory impairment and 28% of the subjects without a manufacturing occupation had olfactory impairment. The p-value is listed as <0.001. How would you explain the meaning of a p-value in this situation to a biology student who had not taken a statistics class?