Small sample difference of two means. The soybean or Dectes stem borer, Dectes t

Question

Small sample difference of two means. The soybean or Dectes stem borer, Dectes texanus texanus LeConte, is a small, gray, long-horned beetle that attacks soybean and wild host plants. An experiment was set up to look at the impact of varieties and treatments on the yield per acre. We will focus on differences of two varieties of soybeans (A and B). There are 12 observations for each variety, which yielded the following data. Summary Statistics Variety A Variety B Mean 47.196 35.415 Std Dev 12.43 12.958 Std Err Mean 3.588 3.741 Upper 95% Mean 55.094 43.648 Lower 95% Mean 39.298 27.182 N 12 12 Sum 566.35 424.98 Variance 154.508 167.904 Skewness -0.012 -0.093 Kurtosis -1.144 -1.37 CV 26.337 36.588 N Missing 0 0 Median 49.555 35.725 Range 39.63 36.99 Interquartile Range 21.195 23.998

The standard error assuming unequal variances is:

SQRT(19.953/19 +34.618/17)

SQRT(26.854/18 + 26.854/16)

SQRT(26.854/19 + 26.854/17)

SQRT(26.854/34)

SQRT(19.953/19 +34.618/17)

SQRT(26.854/18 + 26.854/16)

SQRT(26.854/19 + 26.854/17)

SQRT(26.854/34)

Explanation / Answer

All option are wrong

n1=n2=12 , S1^2 = 154.508 S2^2 = 167.904

Standard Error = SQRT((Sp^2/n1)+(Sp^2/n2))

Sp^2 =(n1-1)S1^2 + (n2-1)S2^2/(n1+n2-2)

Sp^2 =(11*154.508)+(11*167.904)/(22)

Sp^2 = 161.206

Standard error = SQRT(2*(161.206/12))

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