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**AP Statistics Section 15 C**

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**The most common hypothesis about the slope is _________**

The most common hypothesis about the slope is _________. A regression line with slope 0 is _________. That is, the mean of y (does/does not) change when x changes. So this says that there is no true linear relationship between x and y. Put another way, says there is ___________ between x and y in the population from which we drew our data. You can use the test for zero slope to test the hypothesis of zero correlation between any two quantitative variables.

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**Note that testing correlation makes sense only if the observations are ______.**

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The test statistic is just the standardized version of the least-squares slope b. To test the hypothesis compute the t statistic Once again, we use the t-distribution with n - 2 degrees of freedom and as always our p-value is the area under the tail(s). Regressions output from statistical software usually gives t and its two-sided P-value. For a one-sided test, divide the P-value in the output by 2.

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Example 15.6: The hypothesis says that crying has no straight-line relationship with IQ. The scatterplot we constructed shows that there is a relationship so it is not surprising that the computer output given on the previous page of notes give t = ______ with a two-sided P-value of _____. There is (strong/weak) evidence that IQ is correlated with crying.

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**Example 15. 7: A previous example (3**

Example 15.7: A previous example (3.5) looked at how well the number of beers a student drinks predicts his or her blood alcohol content (BAC). Sixteen student volunteers at Ohio State University drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their BAC. Here are the data. Student: 1 2 3 4 5 6 7 8 Beers: 9 BAC: 0.10 0.03 0.19 0.12 0.04 0.095 0.07 0.06 10 11 12 13 14 15 16 0.02 0.05 0.085 0.09

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Here is the Minitab output for the blood alcohol content data: The regression equation is BAC = Beers S = R-Sq = 80.0% Note: the actual calculated values are slightly different from these Predictor Coef StDev T P Constant -1.00 0.332 Beers 7.48 0.000

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**Test the hypothesis that the number of beers has no effect on BAC**

Test the hypothesis that the number of beers has no effect on BAC. Hypotheses: The population of interest is __________________ H0: _______ In words, ____________________________ H1: _______ In words, _________________________________ where is ___________________________

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**Conditions: Calculations:**

7.48

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Interpretation:

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1 1 Slide The Simple Linear Regression Model n Simple Linear Regression Model y = 0 + 1 x + n Simple Linear Regression Equation E( y ) = 0 +

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