Based on data from the U.S. Census Bureau, the National Association of Home Buil

Question

Based on data from the U.S. Census Bureau, the National Association of Home Builders forecasts a rise in homeownership rates for this decade. Part of the forecast is to predict new housing starts by region. The following table shows what they are forecasting. Do the data present sufficient evidence to reject the hypothesis that the distribution of housing starts across the region is the same for all years? Use = .05.

(a) Find the test statistic. (Give your answer correct to two decimal places.)


(ii) Find the p-value. (Give your answer bounds exactly.)
< p <
(b) State the appropriate conclusion.
A. Reject the null hypothesis, there is significant evidence that the distribution of housing starts across the regions is different among the years.

B. Reject the null hypothesis, there is not significant evidence that the distribution of housing starts across the regions is different among the years.    

C. Fail to reject the null hypothesis, there is significant evidence that the distribution of housing starts across the regions is different among the years.

D. Fail to reject the null hypothesis, there is not significant evidence that the distribution of housing starts across the regions is different among the years.

Average Housing Starts Region 1996-2000 2001-2005 2006-2010 Northeast 135 166 180 South 718 704 702 Midwest 312 339 306 West 364 365 389

Explanation / Answer

here applying chi square test :

a)  test statistic =8.9429

(ii) p value : 0.1 < p<0.20

b) as p value is higher then 0.05 level option D is correct

D. Fail to reject the null hypothesis, there is not significant evidence that the distribution of housing starts across the regions is different among the years.

Observed O 1996-2000 2001-2005 2006-2010 Total northeast 135 166 180 481 south 718 704 702 2124 midwest 312 339 306 957 west 364 365 389 1118 Total 1529 1574 1577 4680 Expected E=rowtotal*column total/grand total 1996-2000 2001-2005 2006-2010 Total northeast 157.147 161.772 162.081 481 south 693.931 714.354 715.715 2124 midwest 312.661 321.863 322.476 957 west 365.261 376.011 376.728 1118 Total 1529 1574 1577 4680 chi square xxx 1996-2000 2001-2005 2006-2010 Total northeast 3.1213 0.1105 1.9812 5.213 south 0.8348 0.1501 0.2628 1.248 midwest 0.0014 0.9124 0.8418 1.756 west 0.0044 0.3224 0.3998 0.727 Total 3.962 1.495 3.486 8.9429

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