Question

Small sample difference of means problem. The pathogen Phytophthora capsici causes Bell peppers to wilt and die. It is thought that too much water aids the spread of the pathogen. Two fields A and B were studied to compare the mean soil water content for the two fields as given by the data below: Field A Field B Summary Statistics Summary Statistics Мean 12.528571 Мean 10.76875 Std Dev Std Dev 2.3940402 2.4010328 Std Err Mean 0.6398342 Std Err Mean 0.6002582 13.910849 Upper 95% Mean Upper 95% Mean 12.04817 Lower 95% Mean Lower 95% Mean 11.146294 9.48933 N 14 N 16 Sum 175.4 Sum 172.3 5.7314286 Variance Variance 5.7649583 Skewness 0.4376833 Skewness 0.413672 Kurtosis -1.55338 Kurtosis -1.627369 CV 19.108645 CV 22.2963 N Missing N Missing Minimum 9.9 Minimum 7.1 Maximum 16.6 13.9 Maximum Median 11.45 Median 11.75 Range 6.7 Range Interquartile Range 6.8 Interquartile Range 4.775 4.425 b. What is the standard error for a difference of means test assuming equal variances? Use the pooled variance when calculating the standard error for your answer. Use 4 decimal places and use the proper rules of rounding.

Answer 1

Solution:
Given:

Field A Summary Statistics Field B Summary Statistics Mean Std Dev Std Err Mean Upper 95% Mean Lower 95% Mean 12.528571 2.3940402 0.6398342 13.910849 11.146294 10.76875 2.4010328 0.6002582 12.04817 9.48933 Mean Std Dev Std Err Mean Upper 95% Mean Lower 95% Mean N Sum Variance Skewness Kurtosis 14 Sum Variance Skewness Kurtosis 175.4 5.7314286 0.4376833 -1.55338 19.108645 172.3 5.7649583 -0.413672 -1.627369 22.2963 CV CV N Missing Minimum Maximum Median Range Interquartile Range 9.9 16.6 11.45 N Missing Minimum Maximum Median Range Interquartile Range 7.1 13.9 11.75 6.7 6.8 4.775 4.425

We have to find the standard error for a difference of means test assuming equal variances.

First find Pooled Variance = S_p²

s? 52_(ni - 1) X si + (n2 - 1) ni+n2 - 2

From above table , we have:

n₁ = 14 ,

n₂ = 16

s₁² = 5.7314286

s₂² = 5.7649583

Thus

(14 - 1) ~ 5.7314286 + (16 - 1) ~ 5.7649583 14 + 16 - 2

s_p² = ( 13 X 5.7314286 +15 X 5.7649583 ) / 28

s_p² = ( 74.5085718 + 86.4743745 ) / 28

s_p² = 160.9829463 / 28

s_p² = 5.74939094

Thus pooled estimate of standard error for a difference of means test assuming equal variances is:

ds ='s

S_p = square root of ( 5.74939094 )

S_p = 2.3977888

S_p = 2.3978