Question

Question 1 10 pts Each year, the study Monitoring the Future: A Continuing Study of American Youth (MTF) surveys 12th-grade students on a wide range of topics related to behaviors, attitudes, and values. It is a major source of information on smoking, drinking, and drug habits of American youth. Suppose we want to investigate whether the environment in which students grow up is linked to the likelihood that they have consumed alcohol (more than just a few sips). We focus on three growing-up environments - a farm, the country, or a small-to-medium size city. The two-way table shows the results on these questions from the 2011 MTF survey. Count NO Yes Alcohol Environment Country 342 800 A Farm 144 305 Small Medium City 1366 3049 Do the data provide convincing evidence of an association between the environment in which students grow up and alcohol consumption? Follow the 4-step process. HTML Editor BIVA -I EE : x x ! E V CV TT: 12pt Paragraph

Answer 1

Ho: given two variable are independent
H1: Given two variables are not independent

Chi-Square Test of independence
	Observed Frequencies
	afarm	country	city				Total
no	144	342	1366				1852
yes	305	800	3049				4154
Total	449	1142	4415				6006
	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	afarm	country	city				Total
no	449*1852/6006=138.453	1142*1852/6006=352.145	4415*1852/6006=1361.402				1852
yes	449*4154/6006=310.547	1142*4154/6006=789.855	4415*4154/6006=3053.598				4154
Total	449	1142	4415				6006

(fo-fe)^2/fe	afarm	country	city				total
no	0.222	0.292	0.016				0.530
yes	0.099	0.130	0.007				0.236

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   0.766  
      
Level of Significance =   0.05  
Number of Rows =   2  
Number of Columns =   3  
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 3- 1 ) =   2  
      
p-Value =   0.682   [Excel function: =CHISQ.DIST.RT(χ²,df) ]
Decision:    p value > α , do not reject Ho  

so, there is no association between enviorment and alcohol consumption

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