Download Statistical Inference and Hypothesis Testing: Homework 5 - Prof. Yulia Dementieva and more Assignments Mathematics in PDF only on Docsity! HOMEWORK # 5 Chapter 1, Section 1.6: Sampling Distributions Chapter 1, Section 1.7: Making Inferences Due Date: March 10, 2007 1. Suppose that the thickness of a part used in a semiconductor is its critical dimension and that the process of manufacturing these parts is considered to be under control if the true population variation among the thicknesses of the parts is given by a standard deviation not greater than = 0.60 thousandth of an inch. To keep a check on the process, random samples of size 20 are taken periodically, and it is regarded to be “out of control” if the probability that s 2 will take on a value greater than or equal to the observed sample value is 0.01 or less. What can one conclude about the process if the standard deviation of such a periodic random sample s = 0.84 thousands of an inch? 2. Achievement test scores of all high school seniors in a state have mean 60 and variance 64. A random sample of 100 students from one large high school had a mean score of 58. Is there evidence to suggest that this high school is inferior? (Calculate the probability that the sample mean is at most 58). 3. If 41% of the U.S. population has blood type A, what is the probability that among 200 randomly selected individuals less than 50 will have blood type A? 4. The distributions of systolic and diastolic blood pressures for females diabetics between the ages of 30 and 34 have normal distributions with unknown means. However, their standard deviations are S = 11.8 mm Hg and D = 9.1 mm Hg, respectively. a) A random sample of 10 women is selected from this population. The mean systolic blood pressure for the sample is 130 mm Hg. Calculate a two-sided 95% confidence interval for S, the true mean systolic blood pressure. b) Interpret this confidence interval. c) The mean systolic blood pressure for the sample of size 10 is 84 mm Hg. Calculate a two-sided 90% confidence interval for D, the true mean diastolic blood pressure of the population. d) Calculate a two-sided 99% confidence interval for D. e) How does 99% confidence interval compare to 90% interval? Why? 5. A precision instrument is guaranteed to read accurately to within 2 units. A sample of four instrument readings on the same object yielded the measurements 353, 351, 351, and 355. Find a 90% confidence interval for the population variance assuming that the measurements are normally distributed. Does the guarantee seem reasonable?
