概率统计(英文)chapter 7修改 Statistical Intervals Based on a Single Sample.pptVIP

7. Statistical Intervals Based on a Single Sample 7.1 Basic Properties Confidence Intervals Other Levels of Confidence Suppose we want a 99% CI rather a 95% interval. Rather than starting with a probability of 0.95, we must begin with a probability of 0.99. DEFINITION: A 100(1- )% confidence interval for the mean of a normal population when the value of σ is known is given by or , equivalently, by Example 7.12 Consider the following sample of fat content of n=10 randomly selected hot dogs 25.2 21.3 22.8 17.0 29.8 21.0 25.5 16.0 20.9 19.5 Assuming that these were select from a normal population distribution, a 95% CI for the population mean fat content is PROPOSITION: A prediction interval (PI) for a single observation to be selected from a normal population distribution is the prediction level is Tolerance Intervals Let k be a number between 0 and 100. A tolerance interval for captur-ing at least k% of the values in a normal population distribution with a confidence level 95% has the form Tolerance critical values for k=90.95, and 99 in combination with various sample size are given in Appendix Table A.6. This table also include critical values for a confidence level of 99%. Replacing by +give an upper tolerance bound . Critical values for obtaining these onesided bounds also appear in Appendix Table A.6 7.4 Confidence intervals for the variance and standard deviation of a normal population Example7.10: The slant shear test is the most widely accepted procedure for assessing the quality of a bond between a repair materials and its concrete substrate. The article “Testing the Bond Between Repair Materials and Concrete Substrate” reported that in one particular investigation, a sample of 48 shear strength observations gave a sample mean strength of 17.17 and a s