Question

Living Data Set:

Female - Dorm (90 females), Apt (85 females), Parents (87 females), Other (32 females)
Male - Dorm (71 males), Apt (83 males), Parents (48 males), Other (44 males)
In the living data set, male and female college students were sampled separately and surveyed about their living arrangements. Test at the 5% level to see if the distribution of living arrangement differs for men and women.
Create a contingency table for the Living data set and carry out the Chi-square test of Homogeneity of proportions for the Living data.

Consider using a significance level of .05 for the Living data. Since the p-value is (greater/less) than .05, we (fail to reject/reject) the null hypothesis.
a. The most appropriate conclusion for the test based on the Living datais
b. There is not enough evidence to conclude that the distribution of living arrangement differs for men and women.
c. There is enough evidence to conclude that the distribution of living arrangement differs for men and women.
d. There is enough evidence to conclude that the distribution of living arrangement is the same for men and women.

Answer 1

Perform a Chi-square test of Homogeneity to see if the distribution of living arrangements differs for men and women.

Step-by-step explanation:

To test if the distribution of living arrangements differs for men and women, we can perform a Chi-square test of Homogeneity. First, we create a contingency table with the observed frequencies for each living arrangement category for males and females. Then, we calculate the expected frequencies assuming the null hypothesis is true. Next, we calculate the Chi-square test statistic by summing the squared differences between the observed and expected frequencies divided by the expected frequencies. Finally, we compare the obtained Chi-square test statistic to the critical Chi-square value at the 5% level of significance to determine if we reject or fail to reject the null hypothesis.

The most appropriate conclusion for this test based on the living data set is:

c. There is enough evidence to conclude that the distribution of living arrangement differs for men and women.