STAT 307 Homework #5 Spring 2008 URI Note: Due Monday 3/31/08 - All questions should be handed in. - Selected QUESTIONS will be graded. 1. A research physician wants to estimate the average age of people with diabetes. She took a random sample of 35 diabetics and obtained a mean age of 55.4. a. Find a 95% confidence interval for the mean age μ of people with diabetes. Assume that σ = 21.2 years. b. Interpret your answer from part (a) c. Find a 99% confidence interval for μ. d. Why is the confidence interval you found in part (c) longer that the one in part (a). e. Which confidence interval yields a more precise estimate of μ? Explain your answer. 2. The US National Center for Health Statistics estimates mean weights of Americans by age, height, and sex. Forty U.S. women, 5 ft 4 in. tall and age 18-24, are randomly selected and it is found that their average weight is 136.88 lbs. a. Assuming the population standard deviation of all such weights is 12.0 lb, determine a 70% confidence interval for the mean weight μ, of all U.S. women 5 ft 4 in. tall and in the age group 18-24 years. b. Interpret your answer in part (a). 3. Ehlers, Maercker and Boss studied various characteristics of political prisoners from 2 the former East Germany and presented their findings in the paper “Posttraumatic Stress Disorder (PTSD) Following Political Imprisonment: The Role of Mental Defeat, Alienation and Perceived Permanent Change”. According with the article, the mean duration of imprisonment for 32 patients with chronic PTSD was 33.4 months. Assuming that σ=42 months, a. Determine a 95% confidence interval for the mean duration of imprisonment μ of all East German political prisoners wit chronic PTSD. Interpret your answer in words b. In part (a) you found a 95% confidence interval for the mean duration of imprisonment μ of all East German political prisoners with chronic PTSD. Determine the margin of error, E. c. Explain the meaning of E in this context in terms of the accuracy of the estimate. d. Find the sample size required to have a margin of error of 12 months and a 99% confidence level. e. Determine a 99% confidence interval for the mean duration of imprisonment μ if a sample of the size determined in part (d) has a mean of 36.2. 4. Cadmium is toxic to animals. Mushrooms however are able to absorb and accumulate cadmium at high concentrations. The Czech and Slovak governments have set a safety limit for Cadmium in dry vegetables at 0.5 part per million (ppm). Melgar et. al. measured the cadmium levels in a random sample of the edible mushroom Boletus Pinicola and published the results in the Journal of Environmental Science and Health. A hypothesis test is to be performed to decide whether the mean cadmium level in Boletus Pinicola mushrooms is greater than the government’s recommended limits. a. Determine the null hypothesis 3 b. Determine the alternative hypothesis c. Classify the hypothesis test as two-tailed, left-tailed or right-tailed. 5. The Food and Nutrition Board of the National Academy of Sciences states that the recommended daily allowance (RDA) of iron for adult females under the age of 51 is 18 mg. A hypothesis test is to be performed to decide whether adult females under the Age of 51 are, on average, getting less than the RDA of 18 mg of iron. a. Determine the null hypothesis b. Determine the alternative hypothesis c. Classify the hypothesis test as two-tailed, left-tailed or right-tailed. 6. Refer to exercise 5. The following iron intakes, in milligrams, were obtained during a 24-hour period for 45 randomly selected adults females under the age of 51 and the mean iron intake of the sample was 14.68. At the 1% significance level do the data suggest that adult females under the age of 51 are, on average, getting less than the RDA of 18 mg of iron? Assume that the population standard deviation is 4.2 mg.