Test for Homogeneity Quiz

PDF page 490: The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to draw a conclusion about whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. NOTE The expected value inside each cell needs to be at least five in order for you to use this test.

PDF page 490: Ha: The distributions of the two populations are not the same. Test Statistic 2 Use a χ test statistic. It is computed in the same way as the test for independence. Degrees of Freedom (df) df = number of columns - 1 Requirements All values in the table must be greater than or equal to five. Common Uses Comparing two populations. For example: men vs. women, before vs. after, east vs. west. The variable is categorical with more than two possible response values.

PDF page 490: The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to draw a conclusion about whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. NOTE The expected value inside each cell needs to be at least five in order for you to use this test.

PDF page 490: The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to draw a conclusion about whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. NOTE The expected value inside each cell needs to be at least five in order for you to use this test.

PDF page 490: Ha: The distributions of the two populations are not the same. Test Statistic 2 Use a χ test statistic. It is computed in the same way as the test for independence. Degrees of Freedom (df) df = number of columns - 1 Requirements All values in the table must be greater than or equal to five. Common Uses Comparing two populations. For example: men vs. women, before vs. after, east vs. west. The variable is categorical with more than two possible response values.

PDF page 490: Ha: The distributions of the two populations are not the same. Test Statistic 2 Use a χ test statistic. It is computed in the same way as the test for independence. Degrees of Freedom (df) df = number of columns - 1 Requirements All values in the table must be greater than or equal to five. Common Uses Comparing two populations. For example: men vs. women, before vs. after, east vs. west. The variable is categorical with more than two possible response values.

PDF page 490: Ha: The distributions of the two populations are not the same. Test Statistic 2 Use a χ test statistic. It is computed in the same way as the test for independence. Degrees of Freedom (df) df = number of columns - 1 Requirements All values in the table must be greater than or equal to five. Common Uses Comparing two populations. For example: men vs. women, before vs. after, east vs. west. The variable is categorical with more than two possible response values.

PDF page 491: Do male and female college students have the same distribution of living arrangements? Use a level of significance of 0.05. Suppose that 250 randomly selected male college students and 300 randomly selected female college students were asked about their living arrangements: dormitory, apartment, with parents, other. The results are shown in Table 11.17. Do male and female college students have the same distribution of living arrangements?

PDF page 491: Do male and female college students have the same distribution of living arrangements? Use a level of significance of 0.05. Suppose that 250 randomly selected male college students and 300 randomly selected female college students were asked about their living arrangements: dormitory, apartment, with parents, other. The results are shown in Table 11.17. Do male and female college students have the same distribution of living arrangements?

PDF page 491: df = number of columns – 1 = 4 – 1 = 3

PDF page 491: 2 Calculate the test statistic: χc = 10.129

PDF page 492: at 95% level of confidence, α = 0.05, 7.815. The graph also marks the calculated χ test statistic of 10.129. Comparing the test statistic with the critical value, as we have done with all other hypothesis tests, we reach the conclusion.

PDF page 492: Make a decision: Because the calculated test statistic is in the tail we cannot accept H0. This means that the distributions are not the same.