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Inferences on p class

# When an airplane deviates from the localizer it is

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Unformatted text preview: the localizer (certain distance left and right of the runway). When an airplane deviates from the localizer, it is called an exceedence. an Suppose in a random sample of 250 landings for a certain airline, 30 exceed the runway. Estimate the percentage of exceedences with a 95% confidence interval. With a 99% confidence interval. interval. G. baker, Department of Statistics G. University of South Carolina; Slide 15 Effect of Level of Confidence on a Effect Confidence Interval Confidence For a given sample size, as one increases the level of confidence, what happens to the width of the confidence interval? the What is the consequence of this change in interval width? interval G. baker, Department of Statistics G. University of South Carolina; Slide 16 Effect of Sample Size on a Effect Confidence Interval Confidence At a given level of confidence, as one increases the sample size what happens to the width of the confidence interval? the So choose your sample size before you estimate a proportion with a confidence interval interval G. baker, Department of Statistics G. University of South Carolina; Slide 17 Sample Size ˆ ˆ p (1 − p ) n Maximum Error = e = zα/2 (solving for n) 2 ˆ ˆ zα / 2 p (1 − p) n= 2 e G. baker, Department of Statistics G. University of South Carolina; Slide 18 Sample Size If you can’t guess a value for If 2 ˆ p : 2 zα / 2 (.5)(.5) zα / 2 n= =2 2 e 4e What sample size would you recommend to estimate the proportion of exeedences with a 95% confidence interval and maximum error of 2%? maximum G. baker, Department of Statistics G. University of South Carolina; Slide 19 Research Update! Recent research shows that we get better coverage for (1-α)100% CI’s on coverage p-hat if we alter the CI formula. 95%CI: 95%CI: where where ˆ p ± zα / 2 x+2 ˆ p= n+4 ˆ ˆ p (1 − p ) n+4 (Agresti/Coull) G. baker, Department of Statistics G. University of South Carolina; Slide 20 Statistical Hypothesis A statistical hypothesis iis an assertion or s statistical conjecture concerning one or more population parameters. population Exa...
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