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 100 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 frequency, f\nnot a high school graduate 33\nhigh school graduate 40\ncollege (1 year or more) 27\n\\(\\chi_{0}^{2}=7.378\\) (round to three decimal places as needed.)\nchoose the correct rejection region below.\na. \\(\\chi^{2}\\geq\\chi_{0}^{2}\\) b. \\(\\chi^{2}=\\chi_{0}^{2}\\) c. \\(\\chi^{2}>\\chi_{0}^{2}\\) d. \\(\\chi^{2}<\\chi_{0}^{2}\\)\n(c) calculate the test statistic.\n\\(\\chi^{2}=2.539\\) (round to three decimal places as needed.)\n(d) decide whether to reject or fail to reject the null hypothesis. then interpret the decision in the context of the original claim.\n\\(h_{0}\\). at a 2.5% significance level, there enough evidence to reject the claim that the distribution of educational attainment responses uniform.

Answer

# Explanation: ## Step1: Recall hypothesis - testing rules In a chi - square goodness - of - fit test for a uniform distribution, the null hypothesis $H_0$ is that the distribution is uniform and the alternative hypothesis $H_1$ is that the distribution is not uniform. The test is right - tailed. We reject $H_0$ when $\chi^{2}>\chi_{0}^{2}$. ## Step2: Compare test statistic and critical value We are given $\chi_{0}^{2}=7.378$ (critical value) and $\chi^{2}=2.539$ (test statistic). Since $2.539<7.378$, we fail to reject the null hypothesis. # Answer: Fail to reject; is not; is