Ch13Exampl13_2

Ch13Exampl13_2 - Chapter 13 Section 1 Example 2 The...

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1 Chapter 13 Section 1 Example 2 The chi-square distributions are a family of distributions that take only positive values and are skewed to the right. A specific chi-square distribution is specified by one parameter, called the degrees of freedom. The figure shows the density curves for three members of the χ 2 family of distributions. As the degrees of freedom increase, the density curves become less skewed and larger values become more probable. Table E in the back of the book gives critical values for chi-square distributions. You can use Table E if software does not give you P-values for a 2 test. The chi-square density curves have the following properties: 1. The total area under a chi-square curve is equal to 1. 2. Each chi-square curve (except when df = 1) begins at 0 on the horizontal axis, increases to a peak, and then approaches the horizontal axis asymptotically from above. 3. Each chi-square curve is skewed to the right. As the number of degrees of freedom increase, the curve becomes more and more symmetrical and looks more like a normal curve.
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2 We use the χ 2 density curve with n-1 degrees of freedom to calculate the P-value in a goodness of fit test. The following box summarizes the details. EXAMPLE 13.2 RED-EYED FRUIT FLIES Biologists wish to mate two fruit flies having genetic makeup RrCc, indicating that it has one dominant gene (R) and one recessive gene (r) for eye color, along with one dominant (C) and one recessive (c) gene for wing type. Each offspring will receive one gene for each of the two traits
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Ch13Exampl13_2 - Chapter 13 Section 1 Example 2 The...

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