The Goodness ofFit Test Robb T Koether The Goodness ofFit Test The Goodness of Fit Test Lecture 49 Section 14 3 Goodness ofFit Test on the TI 83 The Effect of Sample Size Goodness ofFit Example Assignment Robb T Koether Hampden Sydney College Tue Dec 1 2009 Outline The Goodness ofFit Test Robb T Koether The Goodness ofFit Test Goodness ofFit Test on the TI 83 The Effect of Sample Size 1 The Goodness of Fit Test 2 Goodness of Fit Test on the TI 83 3 The Effect of Sample Size 4 Goodness of Fit Example 5 Assignment Goodness ofFit Example Assignment Outline The Goodness ofFit Test Robb T Koether The Goodness ofFit Test Goodness ofFit Test on the TI 83 The Effect of Sample Size 1 The Goodness of Fit Test 2 Goodness of Fit Test on the TI 83 3 The Effect of Sample Size 4 Goodness of Fit Example 5 Assignment Goodness ofFit Example Assignment The Hypotheses The Goodness ofFit Test Robb T Koether The Goodness ofFit Test Goodness ofFit Test on the TI 83 The Effect of Sample Size Goodness ofFit Example Assignment Example Steps 1 3 1 H0 p1 1 6 p2 1 6 p3 1 6 p4 1 6 p5 1 6 p2 1 6 H1 H0 is false 2 0 05 X O E 2 3 2 E all cells The Hypotheses The Goodness ofFit Test Robb T Koether The Goodness ofFit Test Goodness ofFit Test on the TI 83 The Effect of Sample Size Goodness ofFit Example Assignment Example Step 4 4 Number Observed Expected 2 6 8 1 20 15 2 20 15 3 14 15 4 8 15 5 14 15 6 14 15 TI 83 Chi Square Probabilities The Goodness ofFit Test Robb T Koether The Goodness ofFit Test Goodness ofFit Test on the TI 83 The Effect of Sample Size Goodness ofFit Example Assignment TI 83 Chi square Probabilities Press 2nd DISTR Select 2 cdf Enter the lower endpoint the upper endpoint and the degrees of freedom Press ENTER The probability appears in the display TI 83 Chi Square Probabilities The Goodness ofFit Test Robb T Koether The Goodness ofFit Test Goodness ofFit Test on the TI 83 The Effect of Sample Size Goodness ofFit Example Assignment Practice Find P 23 6 with df 3 Find P 20 225 30 with df 25 Find P 26 10 with df 6 Find the probability that 2512 is within one standard deviation of its mean The Goodness of Fit Test The Goodness ofFit Test Robb T Koether The Goodness ofFit Test In our example we found 2 6 8 Goodness ofFit Test on the TI 83 There are 6 categories 1 6 so there are 5 degrees of freedom The Effect of Sample Size Goodness ofFit Example Assignment The Goodness of Fit Test The Goodness ofFit Test Robb T Koether The Goodness ofFit Test Goodness ofFit Test on the TI 83 The Effect of Sample Size Goodness ofFit Example Assignment Example Steps 5 6 and 7 5 p value 2 cdf 6 8 E99 5 0 2359 6 Accept H0 7 The die is fair Outline The Goodness ofFit Test Robb T Koether The Goodness ofFit Test Goodness ofFit Test on the TI 83 The Effect of Sample Size 1 The Goodness of Fit Test 2 Goodness of Fit Test on the TI 83 3 The Effect of Sample Size 4 Goodness of Fit Example 5 Assignment Goodness ofFit Example Assignment Goodness of Fit Test on the TI 83 The Goodness ofFit Test Robb T Koether The Goodness ofFit Test Goodness ofFit Test on the TI 83 The Effect of Sample Size Goodness ofFit Example Assignment Be careful when using the TI 83 There is a function called 2 Test but it does not perform the goodness of fit test Some TI 84s have a GOF Test function The GOF Test function does perform the goodness of fit test Goodness of Fit Test on the TI 83 The Goodness ofFit Test Robb T Koether The Goodness ofFit Test Goodness ofFit Test on the TI 83 The Effect of Sample Size Goodness ofFit Example Assignment TI 83 Goodness of fit test Put the observed counts in list L1 Put the hypothetical proportions in list L2 Multiply L2 by the sample size and store as L2 These are the expected counts Calculate L1 L2 2 L2 either all at once or step by step Go to LIST MATH and select sum item 5 Enter Ans and press ENTER The value of 2 appears Then use 2 cdf to find the p value Outline The Goodness ofFit Test Robb T Koether The Goodness ofFit Test Goodness ofFit Test on the TI 83 The Effect of Sample Size 1 The Goodness of Fit Test 2 Goodness of Fit Test on the TI 83 3 The Effect of Sample Size 4 Goodness of Fit Example 5 Assignment Goodness ofFit Example Assignment The Effect of Sample Size The Goodness ofFit Test Robb T Koether The Goodness ofFit Test Goodness ofFit Test on the TI 83 The Effect of Sample Size Goodness ofFit Example Assignment In the previous example 1 s and 2 s were overrepresented and 4 s were underrepresented The Effect of Sample Size The Goodness ofFit Test Robb T Koether The Goodness ofFit Test Goodness ofFit Test on the TI 83 The Effect of Sample Size Goodness ofFit Example Assignment In the previous example 1 s and 2 s were overrepresented and 4 s were underrepresented Yet that was not significant The Effect of Sample Size The Goodness ofFit Test Robb T Koether The Goodness ofFit Test Goodness ofFit Test on the TI 83 The Effect of Sample Size Goodness ofFit Example Assignment In the previous example 1 s and 2 s were overrepresented and 4 s were underrepresented Yet that was not significant What if we observed the same proportions but for a larger sample The Effect of Sample Size The Goodness ofFit Test Robb T Koether The Goodness ofFit Test Goodness ofFit Test on the TI 83 The Effect of Sample Size Goodness ofFit Example Assignment In the previous example 1 s and 2 s were overrepresented and 4 s were underrepresented Yet that was not significant What if we observed the same proportions but for a larger sample That is what if we had observed Number Observed Expected 1 200 150 2 200 150 3 140 150 4 80 150 5 140 150 6 140 150 The Effect of Sample Size The Goodness ofFit Test Robb T Koether The Goodness ofFit Test Goodness ofFit Test on the TI 83 The Effect of Sample Size Goodness ofFit Example Assignment In the previous example 1 s and 2 s were overrepresented and 4 s were underrepresented Yet that was not significant What if we observed the same proportions but for a larger sample That is what if we had observed Number Observed Expected 1 200 150 2 200 150 Would it be signficant 3 140 150 4 80 150 5 140 150 6 140 150 Outline The Goodness ofFit Test Robb T Koether The Goodness ofFit Test Goodness ofFit Test on the …
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