Section 6 4 Confidence Intervals for the Population

Section 6 -4 – Confidence Intervals for the Population Variance and Standard Deviation • Estimating Population Parameters

Section 6 -4 – Confidence Intervals for Variance and Standard Deviation In manufacturing, it is necessary to control the amount that a process varies. For instance, an automobile part manufacturer must produce thousands of parts to be used in the manufacturing process. It is important that the parts vary little or not at all. How can you measure, and thus control, the amount of variation in the parts? You can start with a point estimate.

EXAMPLE 2 (Page 347) You randomly select and weigh 30 samples of an allergy medicine. The sample standard deviation is 1. 2 milligrams. Assuming the weights are normally distributed, construct 99% confidence intervals for the population variance and standard deviation. d. f. = 29. Look in Table 6 in Appendix B (or on the hand-out) Find the row for the d. f. = 29 Find the columns for. 005 and. 995.

EXAMPLE 2 (Page 347) You randomly select and weigh 30 samples of an allergy medicine. The sample standard deviation is 1. 2 milligrams. Assuming the weights are normally distributed, construct 99% confidence intervals for the population variance and standard deviation.

EXAMPLE 2 (Page 347) Now that you have the interval for the variance, take the square roots of the endpoints to find the interval for the standard deviation. We are 99% confident that the actual population variance of weights of allergy medicines is between 0. 8 and 3. 2, and that the actual population standard deviation of weights of allergy medicines is between 0. 9 and 1. 8.

EXAMPLE 2 (Page 347) Find the 90% and 95% confidence intervals for the population variance and standard deviation of the medicine weights.

EXAMPLE 2 (Page 347) Find the 90% and 95% confidence intervals for the population variance and standard deviation of the medicine weights.

ASSIGNMENTS Classwork: Page 348; #1 -6 All Homework: Pages 348 -350; #7 -20 All