Final Exam Review for Statistics I - Fall 2003 | 960 211, Exams of Statistics

Download Final Exam Review for Statistics I - Fall 2003 | 960 211 and more Exams Statistics in PDF only on Docsity! 960:211:01 Spring 2003 Elementary Statistics I Review Problems for the Final Exam 1. Know your terms and definitions, and study Quizzes #2 through #4. Use the review sheet for Exam #2 as a study guide for the material in Chapters 4-5. 2. A random sample of 76 children between the ages of 4 and 5 are taken, and their weights were measured. The sample mean was 34.5 pounds, and the sample standard deviation was 2.74 pounds. (a)Compute a 90% confidence interval for the true mean weight of children between the ages of 4 and 5. (b)Compute a 95% confidence interval for the true mean weight of children between the ages of 4 and 5. (c) In reference to parts (a) and (b), which interval is wider? Why is that the case? (d)Compute the needed sample size to estimate the true mean weight of children between the ages of 4 and 5 with a maximum error tolerance of 1 pound at 95% confidence. 3. CNN has just conducted a poll and wants you to analyze the results. Seven hundred people were asked how they felt about possibly starting a new anti- smoking law. Of the 700 asked, 494 responded favorably to the new law. (a)Compute a 95% confidence interval for the true proportion of people who favor a new anti-smoking law. (b)CNN would like to broadcast the results during their evening newscast. They ask that you provide them with the point estimate of the true proportion of people in favor of this new law as well as the sampling error, both in percentage points. 4. An automobile manufacturer has asked you (a very experienced statistical consultant) to help decide how many safety precautions should be built into their new line of cars. To decide whether the current line of cars is suitable, he asks you to monitor several crash tests to see how much damage is done for a typical highway collision. Since building cars costs a lot of money, you can only crash 11 cars. After doing so, you observe an average damage of $4,517.92 with a standard deviation of $942.77. (a)Compute a 95% confidence interval for the true average damage from a typical highway collision for this line of cars. Assume that the population is normal. (b)Do you think this interval meaningful? If not, what could be done to make it more meaningful? 5. A medical researcher wants to show that a new drug actually reduces the length of allergic reactions to tree pollen. The belief is that people with such allergies need 14.7 hours to recover. (a)State the null and alternative hypotheses for this test. (b)A random sample of 40 allergy-stricken individuals is treated with this new drug, resulting in a sample recovery time of 11.9 hours with a standard deviation of 3.4 hours. Conduct the test at the 0.01 level of significance. 1 (c)Compute the p-value for this test. Give an explicit interpretation of this value. 6. Suppose you perform a one-tailed test, and you reject the null hypothesis at some level of significance. Does it follow that you would have rejected the null hypothesis at the same level of significance if you had conducted a two-tailed test instead? 7. A sample of 50 lenses used in eyeglasses yields a sample mean thickness of 3.05 mm and a sample standard deviation of 0.34 mm. The desired true average thickness of such lenses is 3.20 mm. Does the data strongly suggest that the true average thickness of such lenses is something other than what is desired? Use significance level 0.05. Compute the p-value for this test, and interpret it. 8. A forest meteorology experiment reports the following values for soil heat flux of eight plots covered with coal dust. { 34.7, 35.4, 34.7, 37.7, 32.5, 28.0, 18.4, 24.9 } The mean soil heat flux for plots covered only with grass is 29.0. Assuming that the heat flux distribution is approximately normal, does the data suggest that the coal dust is effective in increasing the mean heat flux over that for grass? Use significance level 0.05. 9. Many consumers are turning to generic drugs in order to reduce prescription costs. A survey of 102 doctors showed that only 47 of them knew the generic equivalent of methadone. Does this provide strong evidence for concluding that fewer than half of all doctors know the generic equivalent of methadone? Use significance level 0.01. 10. Do the following review exercises. On pp. 335-357: #1, 3, 5, 7-10; on pp. 426- 428: #1 [only parts (a) and (e)], 2-4, 6, 9. Solutions to all of these problems are in the textbook. FINAL EXAM INFORMATION Monday 05/12/2003 8:00AM -- 11:00AM Van Dyke Hall, Room 211 (College Ave.) Coverage: Chapters 4-7 What to bring with you:  Calculator  Tables A-2 and A-3  Pencils and erasers  Two pages of notes (front and back)  Student ID (no exceptions!)  Coffee (if you wish) 2