Ch 06 Solutions

Chapter 6 Estimation 6.1 Learni ng ac ti vi ty A6 .1 Question: Nation al figures for a blood test result have been collected and the σ for the populatio n is 1.2. Y ou take a sample of 100 observatio ns and find a sample mean of 25 units. Give the 95% confidence interval for the mean. Solution: We are given: population variance, σ 2 = (1.2) 2 sample mean, ¯ x = 25 with sample size, n = 100. T o get a 95% confiden ce interval for the mean, we need: ¯ x ± 1.96 × σ √ n i.e. 25 ± 1.96 × 1.2 10 i.e. 25 ± 0.2352 i.e. 24.7648 to 25.2352 or we can write that the confidence interval is (24.7648, 25.2352). 6.2 Learning ac ti vi ty A6 .2 Look at the ball bearing example again in Section 6.8 but this time read the descriptio n ‘Measureme nts of the diameter of a random sample of 200 ball bearings produced by a machine, showed a mean ¯ x = 0.284, and a standa rd deviation s = 0.042.’ Find the a) 95% and b) 99% confidence intervals for the true mean value of the diameter of bal l bearings. (Note: Althou gh this time you have been told that your figure for variance is a sample estimate, you justify using the Normal distribution because of the Central Limit Theorem since the sample size is very large and your confidence interval will be exactly the same as in the previ ous example.) 1

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Ch 06 Solutions