Question

CENGAGE MINDTAP Complete: Chapter 17 Problem Set ALU, We waw c e , this page you eu.LIC TRIGE 4. The chi-square test for goodness of fit - No difference from a known population Aa Aa Suppose you are reading a study conducted in the year 2000 about welfare recipients in the United States. The authors report the following frequency data on the household size of the 2,352 welfare recipients in their random sample: Observed Frequencies Household Size 5-or-more-person 4-person 3-person 2-person 1 person 400 329 7 53 588 You wonder if welfare recipients tend to live in different sized households than the U.S. population at large. You obtain the following data from the 2000 census: Percent Distribution of U.S. Households by Size Household Size 5-or-more-person 4-person 3-person 2-person 1-person 10.83% 14.20% 16.53% 32.63% 25.81% [Sur Hobbs F. & Stoops, N. (2002). Census 2000 special reports: Demographic trends in the 20th century U.S. Crut Bureau You use a chi-square test for goodness of fit to see how well the sample of welfare recipients fits the census data. What is the most appropriate null hypothesis? The distribution of household sizes among welfare recipients is not equal across the five household-size categories. The distribution of household sizes among welfare recipients is the same as that provided by the census data. The distribution of household sizes among welfare recipients is equal across the five household-size categories. The distribution of household sizes among welfare recipients is different from that provided by the census data. O

Answer 1

The most appropriate null hypothesis is:

The distribution of household sizes among welfare recipients is same as that provided by the census data.

Expected frequency: % given*sample size

So for 5 or more person: 0.1083*2352 = 254.72

For 4- person: 0.142*2352 = 333.98

Degrees of freedom= no of groups-1= 5-1 = 4

At alpha= 0.01, for df= 4, the chi square critical value is 13.28 (from the chi square tables)

Because our chi square test statistic is greater than the critical value, we have sufficient evidence to reject the null hypothesis. Therefore we can conclude that proportions differ from the corresponding proportions of all US households.