Question

5. Interpretation of a chi-square test for goodness of fit Suppose you are reading a study conducted in the year 2000 about welfare recipients in the United States. The study consisted of a random sample of 199 welfare recipients, and provides summary statistics about various demographic characteristics of the sample, indluding household size broken down into five categories (one, two, three, four, and five or more persons in the household). You wonder if welfare recipients tend to live in different- sized households than the US population at large. You obtain the following data from the 2000 census: Percent Distribution of US Households by Size Household Size five-or-more-person four-person three-person two-person one-person 10.83% 14.20% 16.53% 32.63% 25.81% [Sourcei Hobbs F.&Stoops. N. (2002). Census 2000 special reports: Demographic trends in the 20th century, US Census Bureau. You use a chi-square test for goodness of fit to see if the distribution among welfare recipients is the same as the distribution among all Americans, as described by the census data. Your data satisfies the requirements for a chi-square test. You conduct the test using o 05 and reject the null hypothesis. You conclude there is a significant difference between the distribution of household sizes among welfare recipients and the distribution of the US population as provided by the census data. The following table shows the hypothetical results of the study. This table displays the observed frequencies in the sample of welfare recipients with the expected frequencies as computed using the census data shown in parentheses

Answer 1

since onserved values are higher in larger or smaller households

A higher proportion of welfare recipients live in either larger households (five-or-more people) or smaller households (one-person) than the general US population.