Use the data for 30 - to 34 -year-olds and 65 - to 69 -year-olds to test whether age and educational attainment are related. Use \(\alpha=0.01\).

(a) identify the claim and state \(H_{0}\) and \(H_{a}\),

(b) find the critical value and identify the rejection region,

(c) find the test statistic,

(d) decide whether to reject or fail to reject the null hypothesis,

(e) interpret the decision in the context of the original claim.

Use the table, which lists the distribution of educational achievement for people in the United States ages 25 and older. It also lists the results of a random survey for two additional age groups.

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Ages Educational attainment 25 and older 30-34 65-69 None-8th grade 4.7% 10 23 9th-11th grade 6.9% 23 26 High school graduate 29.5% 80 136 Some college, no degree 16.6% 56 77 Associate's degree 9.8% 34 41 Bachelor's degree 20.5% 75 78 Master's degree 8.7% 31 41 Professional/doctoral degree 3.3% 11 18