a social service organization reports that th...

a social service organization reports that the level of educational attainment of mothers receiving food stamps is uniformly distributed. to test this claim, you randomly select 97 mothers who currently receive food stamps and record the educational attainment of each. the results are shown in the table on the right. at $alpha = 0.025$, can you reject the claim that the distribution is uniform? complete parts (a) through (d) below.\nresponse\tfrequency, f\nnot a high school graduate\t33\nhigh school graduate\t37\ncollege (1 year or more)\t27\n(b) determine the critical value, $chi_{0}^{2}$, and the rejection region.\n$chi_{0}^{2}=7.378$ (round to three decimal places as needed.)\nchoose the correct rejection region below.\na. $chi^{2}<chi_{0}^{2}$\nb. $chi^{2}geqchi_{0}^{2}$\nc. $chi^{2}leqchi_{0}^{2}$\nd. $chi^{2}>chi_{0}^{2}$

Answer

# Answer: D. $\chi^{2}>\chi_{0}^{2}$ # Explanation: ## Step1: Recall chi - square test rule In a chi - square goodness - of - fit test for a uniform distribution, we reject the null hypothesis when the calculated chi - square test statistic $\chi^{2}$ is greater than the critical value $\chi_{0}^{2}$. The null hypothesis $H_0$ is that the distribution is uniform. The alternative hypothesis $H_1$ is that the distribution is not uniform. For a right - tailed chi - square test (which is the case here when testing for non - uniformity against a uniform distribution), the rejection region is $\chi^{2}>\chi_{0}^{2}$.