a social service organization reports that the level of educational attainment of mothers receiving food…

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(a) state \\(h_0\\) and \\(h_a\\) and identify the claim.\n\\(h_0\\): the distribution of educational attainment responses is uniform.\n\\(h_a\\): the distribution of educational attainment responses is not uniform.\nwhich hypothesis is the claim?\n\\(h_0\\)\n\\(h_a\\)\n(b) determine the critical value, \\(\\chi_0^2\\), and the rejection region.\n\\(\\chi_0^2=\\square\\) (round to three decimal places as needed.)

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(a) state \\(h_0\\) and \\(h_a\\) and identify the claim.\n\\(h_0\\): the distribution of educational attainment responses is uniform.\n\\(h_a\\): the distribution of educational attainment responses is not uniform.\nwhich hypothesis is the claim?\n\\(h_0\\)\n\\(h_a\\)\n(b) determine the critical value, \\(\\chi_0^2\\), and the rejection region.\n\\(\\chi_0^2=\\square\\) (round to three decimal places as needed.)

Answer

Explanation:

Step1: Determine degrees of freedom

There are 3 categories (not a high - school graduate, high school graduate, college 1 year or more), so the degrees of freedom $df=k - 1=3 - 1 = 2$, where $k$ is the number of categories.

Step2: Find the critical value

We are given $\alpha = 0.025$. For a chi - square distribution with $df = 2$ and a right - tailed test (since we are testing if the distribution is not uniform), we look up the value in the chi - square distribution table. The critical value $\chi_{0}^{2}=\chi_{\alpha,df}^{2}=\chi_{0.025,2}^{2}=7.378$.

Step3: Determine the rejection region

The rejection region is $\chi^{2}>\chi_{0}^{2}$, so the rejection region is $\chi^{2}>7.378$.

Answer:

$\chi_{0}^{2}=7.378$, Rejection region: $\chi^{2}>7.378$