Based on data from the U.S. Census Bureau, the National Association of Home Buil
ID: 3316959 • Letter: B
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 Average Housing Starts Region Northeast South Midwest West 1996-2000 148 691 344 374 2001-2005 169 685 313 386 2006-2010 178 708 309 373 (a) Find the test statistic. (Give your answer correct to two decimal places.) (ii) Find the p-value. (Give your answer bounds exactly.) (b) State the appropriate conclusion O Reject the null hypothesis, there is significant evidence that the distribution of housing starts across the regions is different among the years O Reject the null hypothesis, there is not significant evidence that the distribution of housing starts across the regions is different among the years o Fail to reject the null hypothesis, there is significant evidence that the distribution of housing starts across the regions is different among the years Fail to reject the null hypothesis, there is not significant evidence that the distribution of housing starts across the regions is different among the yearsExplanation / Answer
above test result we can analyse using the chi-square test,
Category 1
Category 2
cat3
Row Totals
Group 1
148 (164.75) [1.70]
169 (164.33) [0.13]
178 (165.92) [0.88]
495
Group 2
691 (693.63) [0.01]
685 (691.85) [0.07]
708 (698.53) [0.13]
2084
g3
344 (321.52) [1.57]
313 (320.69) [0.18]
309 (323.79) [0.68]
966
gr3
374 (377.10) [0.03]
386 (376.13) [0.26]
373 (379.77) [0.12]
1133
Column Totals
1557
1553
1568
4678 (Grand Total)
the chi-square statistics value is,
i)The chi-square statistic is 5.7593.
ii) The p-value is .450685
b)
last conclusion is correct.
becuse we fail to reject the null hypothesis
thanks
Category 1
Category 2
cat3
Row Totals
Group 1
148 (164.75) [1.70]
169 (164.33) [0.13]
178 (165.92) [0.88]
495
Group 2
691 (693.63) [0.01]
685 (691.85) [0.07]
708 (698.53) [0.13]
2084
g3
344 (321.52) [1.57]
313 (320.69) [0.18]
309 (323.79) [0.68]
966
gr3
374 (377.10) [0.03]
386 (376.13) [0.26]
373 (379.77) [0.12]
1133
Column Totals
1557
1553
1568
4678 (Grand Total)
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