Inference on Single Mean

# Or calculate p value and draw conclusion g baker

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Unformatted text preview: clusion. or Calculate p-value and draw conclusion. G. Baker, Department of Statistics G. University of South Carolina; Slide 58 University 58 (3) Designate Critical Region Assumes H0: µ = 100 is true 0.05 -4 -3 -2 -1 0 100 -4 -3 -2 -1 0 -1.833 1 2 +1 +2 3 +3 4 Y=avg hp +4 tdf=9 G. Baker, Department of Statistics G. University of South Carolina; Slide 59 University 59 Draw conclusion: t df =9 -4 y − µ0 98.7 − 100 = = = −1.4327 s / n 2.8694 / 10 -3 -2 -1 -1.4327 -1.833 0 1 2 3 4 tdf=9 G. Baker, Department of Statistics G. University of South Carolina; Slide 60 University 60 p-value The p-value iis the probability of getting s the sample result we got or something more extreme. more 0.0928 -4 -3 -2 -1 -1.4327 0 1 2 3 4 tdf=9 G. Baker, Department of Statistics G. University of South Carolina; Slide 61 University 61 p-value P(tdf=9 < -1.4327) = 0.0928 P(t Note: Note: If p-value < α, reject H0. value If p-value > α. Fail to reject H0. value 0.0928 0.05 -4 -3 -2 -1 -1.4327 -1.833 0 1 2 3 4 tdf=9 G. Baker, Department of Statistics G. University of South Carolina; Slide 62 University 62 Average Life of a Light Bulb Historically, a particular light bulb has Historically, had a mean life of no more than 2000 hours. We have changed the production process and believe that the life of the bulb has increased. the Let µ = mean life. Let (1) Set Up Hypotheses α = 0.05 H0: Ha: G. Baker, Department of Statistics G. University of South Carolina; Slide 63 University 63 Average Life of a Light Bulb (2) Collect Data and calculate test statistic: y = 2141 t df =14 n = 15 s = 216 y − µ 0 2141 − 2000 = = = 2.5282 s/ n 216 / 15 0.05 0.0121 -4 -3 -2 -1 0 1 2 3 4 tdf=14 1.761 2.5282 p-value = P(tdf=14 > 2.5282) = 0.0121 G. Baker, Department of Statistics G. University of South Carolina; Slide 64 University 64 Average Life of a Light Bulb State Conclusion: At 0.05 level of significance there is At insufficient evidence to conclude that µ > 2000 hours. B. At 0.05 level of significance there is At sufficient evidence to conclude that µ > 2000 hours. A. G. Baker, Department of Statistics G. University of South Carolina; Slide 65 University 65 Mean Width of a Manufactured Part Test the theory that the mean width of a manufactured part differs from 100 cm. manufactured Let µ = mean width. Let (1) Set up Hypotheses (1) α = 0.05 G. Baker, Department of Statistics G. University of South Carolina; Slide 66 University 66 Mean Width of a Manufactured Part (2,3) Collect data and calculate test statistic. (2,3) Collect y = 105 s = 6 n = 20 t df =19 = p − value = 2 * P(t df =19 .... (4) State conclusion. G. Baker, Department of Statistics G. University of South Carolina; Slide 67 University 67 Given population parameter µ and value µ0: Given and For Ho: µ = µ0 For Ha: µ = µ0 α/2 α/2 Ha H0 Ha: µ > µ0 α H0 Ha: µ < µ0 Ha Ha α Ha H0 G. Baker, Department of Statistics G. University of South Carolina; Slide 68 University 68 There Are Two Errors We Can There Make in a Hypothesis Test Make 1) Reject H0 when H0 iis true. This is call...
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