Question

The pathogen Phytophthora capsici causes bell peppers to wilt and die. Because bell peppers are an important commercial crop, this disease has undergone a great deal of agricultural research. It is thought that too much water aids the spread of the pathogen. Two fields are under study. The first step in the research project is to compare the mean soil water content for the two fields. Units are percent water by volume of soil.

Field A samples, x1: 10.2 10.7 15.3 10.4 9.9 10.0 16.6 15.1 15.2 13.8 14.1 11.4 11.5 11.0

Field B samples, x2: 8.1 8.5 8.4 7.1 8.0 7.1 13.9 12.2 13.4 11.3 12.6 12.6 12.7 12.4 11.3 12.5

(i) Use a calculator to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 =

(ii) Assuming the distribution of soil water content in each field is mound-shaped and symmetric, use a 5% level of significance to test the claim that field A has, on average, a higher soil water content than field B. (a) What is the level of significance?

What is the value of the sample test statistic? (Test the difference μ1 − μ2. Do not use rounded values. Round your final answer to three decimal places.)

Answer 1

i.

= 12.51

s₁ = 2.43

= 10.76

s₁ = 2.42

ii.

Level of significance = 0.05

H₀: μ1 − μ2 = 0

H₁: μ1 − μ2 > 0

Assumption: Equality of variance.

t = 1.981

df = 14+16-2

= 28

p-value = 0.0288 < 0.05 i.e. we can reject the null hypothesis and hence we can conclude that field A has, on average, a higher soil water content than field B.

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