Math 119 – Elementary Statistics Name: ____________________________ Homework #3 – DUE: November 5 1. Given a random variable Y with a mean of 26 and a standard deviation of 5. If samples of 25 are...

Math 119 – Elementary Statistics Name: ____________________________ Homework #3 – DUE: November 5 1. Given a random variable Y with a mean of 26 and a standard deviation of 5. If samples of 25 are randomly selected to form a sampling distribution, a. What is the form of the sampling distribution? b. Find the probability that the mean is greater than 27. c. Find the probability that the mean is between 23 and 27. d. Find the value for y so that P Y y    0.33 . e. Find the value for y so that P Y y    0.75. 2. A final exam in Math 116 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, a. What is the form of the sampling distribution? b. Find the probability that the mean of their test scores is less than 76. c. Find the probability that the mean test score is at least 80. d. Is it unusual to for the mean test score to be more than 80? e. Find the mean test score that would be considered unusually high. f. Find the mean test score that would be considered unusually low. 3. A physician wants to develop criteria for determining whether a patient’s pulse rate is atypical, and she wants to determine whether there are significant differences between males and females. Using sample pulse rates from a study, the male pulse rates can be summarized with the statistics 40, 69.4, 11.3. m m n X s    For females, the statistics are 40, 76.3, 12.5. f f n X s    a. Construct a 95% confidence interval estimate of the mean pulse rate for males. b. Construct a 95% confidence interval estimate of the mean pulse rate for females. 4. A research team is willing to assume that systolic blood pressures in a certain population of males are approximately normally distributed. A simple random sample of 64 males from the population had a mean systolic blood pressure reading of 133 with a standard deviation of 16. a. At the 0.05 level of significance, do these data provide sufficient evidence for us to conclude that the population mean is greater than 130? b. Find a 95% confidence interval for the mean systolic blood pressure. 5. Much discussion has appeared in the medical literature in recent years on the role of diet in the development of heart disease. The serum-cholesterol levels of a group of people who eat a primarily macrobiotic diet are measured. Among 24 of them, aged 20—39, the mean cholesterol level was found to be 175 mg/dL with a standard deviation of 35 mg/dL. a. If the mean cholesterol level in the general population in this age group is 230 mg/dL, then test the hypothesis that the group of people on a macrobiotic diet have cholesterol levels different from those of the general population. Let α = 0.01. b. Construct a 99% confidence interval estimate of the mean cholesterol level.