Ch 15 - Chi-Squared _Categorical Data_

The table below displays the model for the

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Unformatted text preview: 2 312.75 104.25 104.25 34.75 0.47 The p‐value is > 0.50 so we cannot reject the null hypothesis. The data do not refute the theory. In fact, the results look almost too good – Mendel had a fictitious assistant, perhaps fictitious data too? Or did the assumptions not hold? Or did we just observe a very unusual. Try It! Desired Vacation Place The AAA travel agency would like to assess if the distribution of desired vacation place has changed from the model of 3 years ago. A random sample of 928 adults were polled by the polling company Ipsos during this past mid‐May. One question asked was “Name the one place you would want to go for vacation if you had the time and the money.” The table below displays the model for the distribution of desired vacation place 3 years ago and the observed results based on the recent poll. 1 = Hawaii 2 = Europe 3 = Caribbean 4 = Other Totals Model 10% 40% 20% 30% 100% 3 years ago Obs Counts 124 (92.8) 390 (371.2) 125 (105.6) 289 (278.4) 928 from poll a. Give the null hypothesis to test if there has been a significant change in the distribution of desired vacation place from 3 years ago. H0: p1 = 0.10, p2 = 0.40, p3 = 0.20, p4 = 0.30 b. The observed test statistic is nearly 31 and the corresponding p‐value is less than 0.001. Interpret this p‐value in terms of repeated random samples of 928 adults. If repeated random samples of n = 928 adults were obtained and if the distribution of desired vacation place has not changed, we would expect to see an X2 statistic of about 31 or larger in less than 0.1% of the repetitions. Note: the underlined phrase is saying “if the null hypothesis were true”. The biggest discrepancies between the observed counts and expected counts under the null were for Hawaii and then from Caribbean. 210 Test of Homogeneity: Helps us to assess if the distribution for one discrete (categorical) variable is the same for two or more populations. Test of Homogeneity Scenario: We have two populations of interest ‐ say preschool boys and preschool gir...
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