Practise reasoning about the chi-square statistic by connecting larger discrepancies between observed group preferences and expected counts to larger statistic values.
A marketing research consultant for a hotel chain hypothesizes that men and women differ in their color preference for guest rooms. The consultant shows pictures 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 be used to test the consultant's hypothesis. Assuming that the conditions for inference are met, which of the following statements is true for the test?
The null hypothesis for the test is that the proportion of each gender who prefer each color scheme is 31.
The sample size is too small to detect a significant difference in a chi-square test for homogeneity of proportions.
The test is not valid because the sample sizes are not equal.
The more that men and women differ in their color preferences, the larger the chi-square statistic will be.
The test would also be appropriate if 90 married couples had been used for the two samples.
D