please show me step by step instructions of how to solve this problem. I need to

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please show me step by step instructions of how to solve this problem. I need to know for my final exam

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. (i) 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) Expected frequency for the the above table.

First we will find the sum of all the observed frequency = 355 + 414 + 762 + 469 = 2000

Here as we know the probability distribution for all four regions

Expected value for Northwest = 2000 * 19.6% = 392

Expected value for Midwest = 2000 * 23% = 460

Expected value for South = 2000 * 35.4% = 708

Expected value for West = 2000 * 22% = 440

(b) Null HYpothesis : H0 : The Distribution of residents in 2013 region wise is similar to the distribution of residents in US in year 1999..

Alternative Hypothesis : Ha : The distribution of residents in US in year 2013 is significantly different from the distribution of residents in US in year 1999.

(c) HEre we will use chi - square distribution here. Degree of freedom = 4 -1 = 3

Here Chi - square value

X2 = (O- E)2/E

So X2 = 14.1124

Here p - value = CHITEST(Observed, Expected) = 0.0027

So p - value s< 0.01

(iv) Using 0.01 as level of significance we will get critical chi- square value equals to 11.34 so we can reject the null hypothesis and can conclude that The distribution of residents in US in year 2013 is significantly different from the distribution of residents in US in year 1999.

Region Observed (O) Expected(E) (O - E)^2/E NE 355 392 3.4923 MW 414 460 4.6 South 762 708 4.1186 West 469 440 1.9114 Sum 2000 2000 14.1224

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