Question

60. A recent debate about where in the United States skiers believe the skiing is best prompted the following survey. Test to see if the best ski area is independent of the level of the skier. U.S. Ski Area Beginner Intermediate Advanced Tahoe 20 30 40 Utah 10 30 60 Colorado 10 40 50 .

Answer 1

Ho: Best ski area is independent of the level of the skier

      Ha: Best ski area is dependent on the level of the skier

Chi-Square Test of independence
	Observed Frequencies
	0
U.S Ski Area	Beginner	Intermediate	Advanced				Total
Tahoe	20	30	40				90
Utah	10	30	60				100
Colorado	10	40	50				100
Total	40	100	150				290
	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	Beginner	Intermediate	Advanced				Total
Tahoe	40*90/290=12.414	100*90/290=31.034	150*90/290=46.552				90
Utah	40*100/290=13.793	100*100/290=34.483	150*100/290=51.724				100
Colorado	40*100/290=13.793	100*100/290=34.483	150*100/290=51.724				100
Total	40	100	150				290
	(fo-fe)^2/fe
Tahoe	4.6360	0.0345	0.922
Utah	1.0431	0.5828	1.324
Colorado	1.0431	0.8828	0.0575

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   10.526  
      
Level of Significance =   0.1  
Number of Rows =   3  
Number of Columns =   3  
Degrees of Freedom=(#row - 1)(#column -1) = (3- 1 ) * ( 3- 1 ) =   4  
      
p-Value =   0.0324417   [Excel function: =CHISQ.DIST.RT(χ²,df) ]
Decision:    p-value < α , Reject Ho  

conclusion: Best ski area is dependent on the level of the skier