week11-2up_001 - Standard Error of Est NORMALLY distributed...

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STA 2023 c D.Wackerly - Lecture 16 207 Thought: An honest politician is one who, when bought, stays bought.—(Simon Cameron) Assignments : Today: P. 308 – 310, 322 – 326, 328 – 332 For Tuesday: Exercises 7.54, 7.60–7.62, 7.66 8.7, 8.9, 8.10, 8.13 For Wednesday: P. 328 – 332 For Thursday : Exercises 8.18, 8.21–23, 8.25, 8.27 Last Time: SEE FORMULA SHEET Parameter Estimator Standard Error of Est. For “large” sample size, estimators approximately NORMALLY distributed. STA 2023 c D.Wackerly - Lecture 16 208 Last Time: LARGE SAMPLE Confidence Interval for a PARAMETER estimator formula sheet table standard errors formula sheet 1-α α/2 α/2 Population mean, (P. 283), LARGE sample CI: Population Proportion, (P. 300), LARGE sample CI:
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STA 2023 c D.Wackerly - Lecture 16 209 When is “large enough” to Validly construct a LARGE SAMPLE CI for (Project) If ( , ) then (respectively) the binomial distribution histogram is SKEWED RIGHT (SYMMETRIC, SKEWED LEFT). (when is binomial) has an approx normal (symmetric) distn for LARGE . For an approx. norm. dist. var., ALMOST ALL values of the var. are within 3 std. dev. of the mean. KNOW: If is approx normally dist., expect that and Easier to check: larger of smaller of STA 2023 c D.Wackerly - Lecture 16 210 Ex. Took sample of size 40, obtained . Can we validly use the formula to construct a CI for p? ? Choosing the Sample Size to estimate Want: Estimate of that is within “ ” units with confidence level (p. 307) for C.I. and solve for Need : at least a “ballpark value” for
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STA 2023 c D.Wackerly - Lecture 16 211 Finding the sample size to estimate . Want : Estimate for to be correct to within “ units with confidence. standard error and SOLVE for C.I. and solve for (p. 309) Need : at least a “ballpark value” for Ex.: Insecticide designed to kill approx. of insects within 1 hour. How large sample size to estimate true “kill rate” to within to within with probability . Parameter : , , Confidence : STA 2023 c D.Wackerly - Lecture 16 212 What is ? Don’t know but . If you have a “ballpark” value of USE IT !!!
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STA 2023 c D.Wackerly - Lecture 16 213 How about if we have no idea of the value of – THEN WHAT? Higher confidence: bigger smaller bigger bigger smaller bigger bigger bigger .5 .25 .4 or .6 .24 .3 or .7 .21 .2 or .8 .16 .1 or .9 .09 Max value of is at . STA 2023 c D.Wackerly - Lecture 16 214 That is FOR EVERY VALUE OF .
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