Many human characteristics are determined by genetics, but many others are by ou

Question

Many human characteristics are determined by genetics, but many others are by our environment. There are therefore many studies of identical twins who have been raised apart. The table below shows the IQs of ten pairs of twins who were raised apart. In each pair, one twin had been raised in a 'good' environment and another in a 'poor' environment The genetic influence on IQ is evident -when one twin has high IQ, the other often does too. However we can also ask... Do the twins raised in a 'good' environment have a different average IQ from those raised in a 'poor' environment? Test this claim at the .05 level. Make sure to draw a conclusion in plain English. I did have a little trouble with this problem) Ho: there is no significance difference between two means Ha! there is significance difference between two means.

Explanation / Answer

Data:     

n = n1 = n2 = 10    

d-bar = 30.5    

s (of d) = 14.23024947    

Hypotheses:     

Ho: 1 = 2     

Ha: 1 2     

Decision Rule:    

= 0.05    

Degrees of freedom = 10 - 1 = 9

Lower Critical t- score = -2.262157158   

Upper Critical t- score = 2.262157158   

Reject Ho if |t| > 2.262157158   

Test Statistic:     

SE = s/n = 14.2302494707577/10 = 4.5   

t = d-bar/SE = 30.5/4.5 = 6.777777778   

p- value = 8.10612E-05    

Decision (in terms of the hypotheses):    

Since 6.777777778 > 2.262 we reject Ho and accept Ha

There is sufficient evidence that 1 2.

Poor Good d = Good - Poor 100 125 25 65 95 30 60 100 40 125 120 -5 85 120 35 145 185 40 55 80 25 180 210 30 60 105 45 135 175 40 d-bar = 30.5 s = 14.23024947

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