# The U.S. Census Bureau compiles census data on educational attainment of Americans. From the document Current Population Reports

Brennan Flores 2021-09-22 Answered
The U.S. Census Bureau compiles census data on educational attainment of Americans. From the document Current Population Reports, we obtained the 2000 distribution of educational attainment for U.S. adults 25 years old and older. Here is that distribution.
[Table]
A random sample of 500 U.S. adults (25 years old and older) taken this year gave the following frequency distribution.
[Table]
Decide, at the 5% significance level, whether this year’s distribution of educational attainment differs from the 2000 distribution.

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falhiblesw

1. Determine the observed frequencies and the chi-square subtotals:
2. Add all chi-square subtotals:
$$\displaystyle{x}^{{{2}}}={2.674}$$
Determine the critical value using table VII with $$df=c-1=6-1=5$$.
$$\displaystyle{x}^{{{2}}}{0.05}={11.070}$$
If the test statistic $$x^{2}$$ is more than the critical value, then reject the null hypothesis:
$$2.674<11.070 \Rightarrow$$ Do not reject $$H_{0}$$