12. An urban economist wishes to test the claim that the distribution of United

Question

12. An urban economist wishes to test the claim that the distribution of United States residents is different today than it was in 1999. For this purpose he disected the United States into four regions. During 1999 about 19.6% of the population of the United States resided in the Northeast. About 23.0% of the population resided in the Midwest, about 35.4% resided in the South and 22.0% resided in the west. In 2014 the economist randomly selects 2000 households from the US and obtains the following frequency distribution. Region Observed Frequency Expected Frequency Northeast Midwest South West 355 414 762 469 . (i) Compute the expected frequencies for the above table. .(ii) What are the null and the alternative hypotheses? Compute the appropriate test statistic. (ii) What sampling distribution you need to use. What degrees of freedom you may need to consider, if any? Compute the p-value. . (iv) Using 0.01 as the level of significance, what would be the decision of the economist? Explain what the decision means in the context of the problem.

Explanation / Answer

i) see the table above

ii) null: follow the frequency distribution

alternate: does not follow

TS = 14.12235

iii) chi-square

df = 4-1 = 3

p-value =0.00274

since p-value < 0.01

we reject the null hypothesis

there is sufficient evidence that the sample does not follow the distribution

Oi Ei (Oi-Ei)^2/Ei 0.196 355 392 3.492346939 0.23 414 460 4.6 0.354 762 708 4.118644068 0.22 469 440 1.911363636 1 2000 2000 14.12235464 critical value 7.814727903

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