Chap 5 The Normal Distribution Sampling Distributions：第一章5正态分布与抽样分布.ppt

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Chap 5 The Normal Distribution Sampling Distributions：第一章5正态分布与抽样分布.ppt

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66 Confidence intervals use a/2, so divide a! 70 71 Allow students about 20 minutes to solve. 72 73 9 74 76 77 9 78 80 81 82 83 84 95 As a result of this class, you will be able to... 4 9 5 9 10 19 22 26 27 31 32 33 34 35 Notice that the interval width is determined by 1-a in the sampling distribution. 36 Have students explain why each of these occurs. Level of confidence can be seen in the sampling distribution. 44 45 9 46 47 48 49 50 52 53 9 54 56 57 64 Confidence intervals use a/2, so divide a! Confidence Interval Mean (s Known) Assumptions Population standard deviation is known Population is normally distributed If not normal, can be approximated by normal distribution (n 3 30) Confidence interval estimate Estimation Example Mean (s Known) The mean of a random sample of n = 25 is`X = 50. Set up a 95% confidence interval estimate for m if s = 10. Estimation Example Mean (s Known) The mean of a random sample of n = 25 is`X = 50. Set up a 95% confidence interval estimate for m if s = 10. Confidence Interval Solution* Confidence Interval Estimate Mean (s Unknown) Confidence Interval Estimates Confidence Interval Mean (s Unknown) Assumptions Population standard deviation is unknown Population must be normally distributed Use Student’s t distribution Confidence interval estimate Student’s t Distribution 0 t (df = 5) Standard normal t (df = 13) Bell-shaped Symmetric ‘Fatter’ tails Student’s t Table t values a / 2 Assume:n = 3df = n - 1 = 2a = .10a/2 =.05 .05 Student’s t Table Assume:n = 3df = n - 1 = 2a = .10a/2 =.05 2.920 t values a / 2 .05 Estimation Example Mean (s Unknown) A random sample of n = 25 has`X = 50 S = 8. Set up a 95% confidence interval estimate for m. Thinking Challenge You’re a time study analyst in manufacturing. You’ve recorded the following task times (min.): 3.6, 4.2, 4.0, 3.5, 3.8, 3.1. What is the 90% confidence interval estimate of the population mean task time? Alone Group Class Confidence Interval Solution* `X = 3.7