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.)

What is the sample test statistic (2 decimal places) and the P-value of the sample test statistic (4 decimal places)?

Method A 1.15 1.22 1.47 2.26 1.98 1.78 1.12 1.75 1.36 2.07 1.37 Method B 1.26 1.79 1.89 1.32 1.64 1.70 1.44 1.40 2.15 2.30 1.60 1.72

Explanation / Answer

Test Statistic
X(Mean)=1.5936
Standard Deviation(s.d1)=0.395 ; Number(n1)=11
Y(Mean)=1.6842
Standard Deviation(s.d2)=0.3181; Number(n2)=12
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =1.5936-1.6842/Sqrt((0.15603/11)+(0.10119/12))
to =-0.602

P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -0.6024 ) = 0.56

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