ClassNotes5_26_08

# ClassNotes5_26_08 - CHAPTER 10 Confidence Intervals There...

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CHAPTER 10 Confidence Intervals There are two types of estimators in statistcis POINT estimate and INTERVAL estimates A (1 - α) x 100% Confidence Interval for μ Assumptions: 1. Normal Population 2. σ is Known For a 95% Confidence Interval, Zα/2 =1.96 => α=.05 => α/2 = 0.025 0.48 0.48 α/2=0.025 α/2=0.025 0.95 0 Z α/2 Z α/2 10.22 page 319 n= 8, σ=10, 1-α=.95 Ages are as follows: 52, 68, 22, 35, 30, 56, 39, 48 = 43.75+/-6.9 Zα/2 =1.96 => α=.05 If asked to do a 93% interval it would be narrower The higher the confidence interval, the wider that interval gets At 99%, you'd be more confident in it, but have less info on μ 1-α is called a confidence level is called a significance level. + - n Z X n Z X σ σ α α * , * 2 2 n Z X σ α ± 2 8 10 96 . 1 75 . 43 ± n X X n i i - = 1 75 . 43 8 350 1 = = = - n X X n i i

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For 93% interval: Confidence Interval, 1-α=.93, α=.07 => α/2 = 0.035 =>Zα/2 = 1.81 43.75+/-6.46 [37.35, 50.15] **** Important Point--Confidence Intervals are ALWAYS two sided (two-tai Basically, just need to look up the right Z score 10.29 z-Estimate: Mean Column 1 Mean 75.63 Standard Deviation 20.45 Observations 16 SIGMA 15 LCL 65.97 UCL 85.28
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