An urban economist wonders if the distribution of U.S. residents in the U.S. is

Question

An urban economist wonders if the distribution of U.S. residents in the U.S. is different today than it was in 2000. In 2000, 19% of the population resided in the Northeast, 22.9% m the Midwest, 35.6% in the South, and 22.5% in the West. The economist randomly selects 1500 households in the United States and obtains the frequency distribution shown in the table below. She wants to do a Goodness of Fit test to determine if the distribution of residents is deferent today, i.e. she test the hypotheses: H0: distribution of residents in the US is the same as it was in 2000 H_1: distribution of residents in the US is different than it was in 2000 Calculated the expected frequencies for this test. NE = 269, MW = 327, SO = 554, WE = 350 NE = 190, MW = 229, SO = 356, WE = 226 NE = 285, MW = 343.5, SO = 534, WE = 337.5

Explanation / Answer

This is case of the chi square test , as we want to test whether the distribution of the resident is same or different in 2000 , the expected frequency must be the same as what it was in year 2000 , which is

Hence C

If the p value is less than 0.05 then the test is signifcant and we reject the null hypothesis in favor of alternate hypothesis and conclude that the distribution is different today from it was in year 2000.

Ideally , the expected frequency is calculated as

Row total * col total / Total

but here in this case you would notice that we need to check if the distribution is still the same , so if you do n*p from the above table for the expected frequency , n being 1500 ,

Region Observed frequency percent Northeast 269 0.19 Midwest 327 0.229 south 554 0.356 west 350 0.225

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