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Proportions

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Josh Hamilton got 186 hits out of 518 attempts in 2010. What is his batting average? Is this Hamilton’s ABILITY to get a hit? Are you confident that you’ve nailed Hamilton’s ABILTIY ? 186/518 = 0.359 0% confident No, it is only an estimate of Hamilton’s ABILITY.

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A confidence interval has: a center (single-value estimate of an ABILITY ) a margin of error (2 standard deviations) Confidence Interval = center ± margin of error We can predict that 95% of the time, an athlete’s ABILTIY will be within 2 standard deviations of their PERFORMANCE. ★

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Confidence Interval = center ± margin of error Confidence Interval Where P = PERFORMANCE A = ABILITY n = # of attempts You will always be given the formula above. You need to learn how to use it.

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All we have is Hamilton’s PERFORMANCE. Therefore his PERFORMANCE is his estimated ABILITY. Confidence Interval Margin of Error Standard Deviation

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We are 95% confident that Hamilton’s true ABILITY to get a hit is between 0.317 and 0.401.

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Does the interval give convincing evidence that Hamilton’s ABILITY to get a hit in 2010 is greater than 0.300? Explain. Yes All of the plausible values are greater than 0.300.

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TTo estimate an athlete’s ABILITY, we can calculate a confidence interval for a proportion if the data are categorical and we are interested in the proportion of times the athlete is successful. AA confidence interval has two parts: aa single-value estimate (a single number in the middle of an interval that represents our best guess of an athlete’s ABILITY) aa margin of error (an amount which is added to and subtracted from the single-value estimate) TThe formula for the confidence interval of a proportion is: CI

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