Are yields for organic farming different from conventional farming yields? Indep

Question

Are yields for organic farming different from conventional farming yields? Independent random samples from method A (organic farming) and method B (conventional farming) gave the following information about yield of lima beans (in tons/acre). (Reference: Agricultural Statistics, United States Department of Agriculture.) Use a 1% level of significance to test the hypothesis that there is no difference between the yield distributions. What is the level of significance? State the null and alternate hypotheses. Compute the sample test statistic. (Use 2 decimal places.)

Explanation / Answer

Test Statistic
X(Mean)=1.53
Standard Deviation(s.d1)=0.345; Number(n1)=11
Y(Mean)=1.62
Standard Deviation(s.d2)=0.413; Number(n2)=12
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =1.53-1.62/Sqrt((0.69/11)+(0.826/12))
to =-0.2482

P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -0.2482 ) = 0.9837

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