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% in 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 different today, i.e. she test the hypotheses: H_0: distribution of residents in the US is the same as X was in 2000 H_1: distribution of residents in the US is different than it was in 2000 The chi-square statistic calculated for this test is 2.903. What conclusion can you make assuming a significance level of 0.05? (Use df and critical value you selected m previous problem) There is not enough evidence to claim that the distribution of U.S. residents is different than it was in 2000. There is enough evidence to claim that the distribution of U.S. residents is different than it was in 2000. There is not enough evidence to claim that the attribution of U.S. residents is the same as it was in 2000. There la enough evidence to claim that the distribution of U.S. residents is the same as it was in 2000.

Explanation / Answer

Here, given that Chi-square calcuted value is 2.903.

Level of significance is 0.05

degrees of freedom is 4-1=3

In chi-square table we have to see value at 0.05 level of significance with 3 d.f.

Here,tabulated chi-square value=7.814

chi-square calculated value<chi-square tabulated value

Hence we accept the null hypothesis.

Correct option is D.

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