One growing concern regarding the U.S. economy is the inequality in the distribution of income. An economist wants to know if the distribution of income is changing, so she randomly selects 1500 households and obtains the household income shown in Table 2. Table 2 also contains the expected counts under the assumption the distribution has not changed since 2000 (obtained in Example 1). Does the evidence suggest that the distribution of income has changed since 2000 at the \(\alpha=0.05\) level of significance? Note: The data in Table 2 is based on the 2013 Current Population Survey and has been adjusted for inflation.

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Table 2 Income Observed Counts Expected Counts Under $15,000 130 105 $15,000 to $24,999 137 129 $25,000 to $34,999 150 139.5 $35,000 to $49,999 207 214.5 $50,000 to $74,999 291 295.5 $75,000 to $99,999 202 225 At least $100,000 383 391.5