Section 15.1 Inference for Population Spread AP Statistics

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3 Why are changes in standard deviation important? Manufacturer’s need to know that if changes in their processes cause less variation in their outcomes. For example, even though two processes produce the same mean amount of ice cream, the better process has smaller variation.

4 Warning!!! Procedures for inference about the population mean are extremely sensitive to non-normal distribution That is to say, the presence of a non-normal distribution make your conclusion wildly inaccurate even in the presence of large samples That is to say, proceed with extreme caution

5 The F test for comparing two standard deviations

6 The F statistic

7 Comments about the F statistic If sample distributions have the same standard deviation, the value of F is 1. In order to make the table of values smaller and easier to read, we only calculate the F value with the larger standard deviation on top.

8 Comments about the F statistic Because the variances are always positive, F is always positive. The F distribution is skew right.

9 Example An SRS of size 10 is drawn from normal distribution. Its standard deviation is 6. An SRS of size 11 is drawn from normal distribution. Its standard deviation is 5.

10 What is evidence of different standard deviations? When the standard deviations are very different, the F value will be much larger than 1. The F table gives the upper tail probabilities that two samples with the same standard deviation would give such different results by pure chance.

11 F(9,10) Degree of freedom for the numerator Degree of freedom for the denominator

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14 Example Medical experiment to compare the mean effects of calcium and a placebo on the blood pressure of black men. We might also compare the standard deviations to see whether calcium changes the spread of blood pressures among black men.

15 Example Group 1 (Calcium) results:  7, -4, 18, 17, -3, -5, 1, 10, 11, -2  n=10, x-bar=5.000, s=8.743 Group 2 (Placebo) results:  -1, 12, -1, -3, 3, -5, 5, 2, -11, -1, -3  n=11, x-bar=-0.273, s=5.901

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17 Assignment 15.1 to 15.7 odd