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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.

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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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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. O 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.
Transcribed Image Text: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. O 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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