A marketing research consultant for a hotel chain hypothesizes that men and women differ in their color preference for guest rooms. The consultant shows a picture of rooms decorated with three different color schemes to each person in a random sample of 110 men and to each person in a random sample of 90 women. The consultant asks each person to choose his or her favorite color scheme. A chi-square test for homogeneity of proportions will used to test the consultant's hypothesis. Assuming the conditions for inference are met, which of the following statements is true for the test? O The test would be appropriate if 90 married couples had been used for the two samples. O The test is not valid because the sample sizes are not equal O The sample size is too small to detect a significant difference in a chi-square test for homogeneity. The more that men and women differ in their color preferences, the larger the chi-square statistic will be. O The null hypothesis for the test is that the proportion of each gender who prefer each color scheme is 1/3.

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