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Proportions. 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.

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Presentation on theme: "Proportions. 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."— Presentation transcript:

1 Proportions

2 Josh Hamilton got 186 hits out of 518 attempts in  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 = % confident No, it is only an estimate of Hamilton’s ABILITY.

3  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. ★

4 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.

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

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

7 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

8 TTo 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. AA confidence interval has two parts: aa single-value estimate (a single number in the middle of an interval that represents our best guess of an athlete’s ABILITY) aa margin of error (an amount which is added to and subtracted from the single-value estimate) TThe formula for the confidence interval of a proportion is: CI


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