Math 130 - 116 Final Exam A Name___________________________ Instructor________________________ Please show all work and round answers to 3 decimal places unless otherwise requested. Each answer is worth 3 percentage points unless otherwise indicated. 1. 2. True or False (2 points each) a. In an observational study, subjects are assigned to treatment groups at random. ___________ b. Observational studies are generally more reliable than randomized experiments. ___________ c. In a randomized experiment, subjects decide for themselves which treatment they will get. ___________ d. In a double-blind study, neither the investigators nor the subjects know who is getting which treatment. ___________ (2 pts) A radio talk-show host invites listeners to send an email to express their opinions on an upcoming election. More than 10,000 emails are received. What type of sample is this? _____________________ 3. (2 pts each) The Centers for Disease Control and Prevention reported that there were 443,000 smokingrelated deaths in the United States in a recent year. The numbers of deaths caused by various illnesses attributed to smoking are as follows: Illness Number Lung Cancer 128,900 Ischemic Heart Disease 126,000 Chronic obstructive pulmonary disease 92,900 Other 95,200 Total 443,000 a. What is the probability that a smoking-related death was the result of lung cancer? _____________ b. What is the probability that a smoking-related death was not the result of ischemic heart disease? _____________ 4. (2 pts each) A 95% confidence interval for the mean mineral content (in percent) of spinach is found to be (19.5, 21.26). a. What is the margin of error in this confidence interval? _________________________ b. If a 99% confidence interval has been constructed, would the margin of error be greater or less than the one found in part (a)? ________________________ 5. (2 pts) A survey asks the participants their age, gender, email address, income and city in which they live. Name all of the quantitative variables in this survey. _________________________ Page 2 6. (2 pts) The following table represents the number of live births to women age 15 - 44 in the state of Wyoming in a recent year. Find the age range that represents the median for this distribution. Age 15 - 19 20 - 24 25 - 29 30 - 34 35 - 39 40 - 44 Number of live births 795 2410 2190 1208 499 109 ___________ 7. (2 pts) The correlation coefficient, r, was calculated to find the strength of the relationship between the number of hours studied and the grade in a statistics course. (r = .82) What is the explanatory variable in this situation? ___________________ 8. (2 pts) According to the most recent statistics, one in every 34 pregnancies is a twin/triplet. What are the odds of a pregnancy resulting in twins/triplets? ___________________ 9. (4 pts) You would like to find a random sample of 4 patients from a list of 40 patients to take part in an experiment. Use the following list of random digits to find the 4 patient random sample. 99154 70392 79230 31058 92210 70439 08629 73299 01696 30913 12835 _____________________ 10. The National Health and Nutrition Examination Survey (NHANES) reported that in a recent year, the mean serum cholesterol level for U.S. adults was 202, with a standard deviation of 41 (the units are milligrams per deciliter). Simple random sample of 110 adults is chosen. a. What is the probability that the sample mean cholesterol is greater than 210? _____________ b. What is the probability that the sample mean cholesterol level is between 190 and 200? _____________ Page 3 11. The following stem-and-leaf plot represent the weights of 30 college freshman males (in pounds): 12 | 4449 13 | 36 14 | 3589 15 | 01556778 16 | 001336 17 | 12 18 | 2 19 | 225 a. (5 pts) Find the five-number summary for this data using appropriate values for this data. ________________________________ b. (4 pts) Any outliers would be below ____________ or above ____________ 12. A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights of babies born the state of New York. The mean weight was 3234 grams with a standard deviation of 871 grams. Assume that the birth weight data are approximately normal. Use the 68 - 95 - 99.7 rule to answer the following: a. What proportion of newborn babies weigh between 2363 and 4105 grams? ___________________ b. What proportion of newborn babies weigh less than 1492 grams? ___________________ 13. Clearly define a Sampling Distribution and explain what the Central Limit Theorem tells us about sampling distributions. Page 4 14. The Centers for Disease Control and Prevention reported that diastolic blood pressures of adult women in the United States are approximately normally distributed with mean 80.5 millimeters of Mercury and standard deviation 9.9 mm Hg. a. Find the proportion of adult women who have diastolic blood pressure of more than 78 mm Hg. _____________ b. Find the diastolic blood pressure range for the middle 70% of adult women. _____________ c. 25% of adult women have a diastolic blood pressure above what amount? _____________ 15. A machine that fills cereal boxes is supposed to put 20 ounces of cereal in each box. A simple random sample of 6 boxes is found to contain a sample mean of 20.25 ounces of cereal. It is known from past experience that the fill weights are normally distributed with a standard deviation of 0.2 ounces. a. Construct a 90% confidence interval for the mean fill weight. ________________________ b. Using the 90% confidence interval find the sample size that would result in a margin of error of less than 0.05 ounces. _________________________ 16. In a sample of 123 hip surgeries of a certain type, the average surgery time was 136.9 minutes with a standard deviation of 22.6 minutes. Construct a 95% confidence interval for the mean surgery time for this procedure. ________________________ Page 5 17. (10 points) The following display from a TI-84 calculator presents the results of a hypothesis test for a population mean . 2.0 t = -2.424366107 p = .013385940 = 1.88 Sx = .21 n = 18 a. State the null and alternative hypotheses. H0: ______________ Ha: _____________ b. How many degrees of freedom are there? _____________ c. Do you reject Ho at = .05? Explain. ___________________ __________________________________________________________________________ d. Someone want to test the hypothesis Ho: = 1.8 versus Ha: >1.8. Use the information in the original display above to compute the t-statistic for this test. ___________________ e. Compute the P-value for the test described in part (d). f. Can the null hypothesis in part (d) be rejected at = .05? Explain. ___________________ ____________ __________________________________________________________________________ 18. (6 pts) A Pew poll taken in 2010 surveyed 800 people aged 18 - 29 and found that 166 of them had one or more tattoos. Conduct a hypothesis test with = .01 to find whether the percentage of people aged 19 - 29 who have a tattoo is less than 25%. Fill in the required parts of the test below: Hypotheses: Test and Test Statistic: P-Value: Conclusion: Page 6 19. (6 pts) The National Health Statistics Reports published recently reported the following information about the weight of one-year-old boys and girls: Boys Girls Mean weight in pounds 25.5 24.1 Standard deviation 5.3 4.3 n 360 328 Perform an appropriate statistical test to determine whether the mean weight of girls is less than the mean weight of boys. Use = .05. Hypotheses: Test and Test Statistics: P-Value: Conclusion: 20. A blood pressure measurement consists of two values: the systolic pressure, which is the maximum pressure taken when the heart is contracting, and the diastolic pressure, which is the minimum pressure taken at the beginning of the heartbeat. Blood pressures were measured, in millimeters, for a sample of 12 adults. The following table presents the results? Systolic Diastolic 134 87 115 83 113 77 123 77 119 69 118 88 130 76 116 70 154 94 157 103 105 66 108 69 a. Compute the correlation coefficient between systolic and diastolic blood pressure ___________________ b. Find the equation of the regression line using x = systolic pressure. ___________________ Bonus: A research agency wants to conduct a poll to determine a confidence interval for the proportion of people who visit the dentist at least once per year. What random sample size is needed in order to determine a 98% confidence interval with a margin of error of 4.9%