The pathogen Phyotphthora capsici causes bell peppers to wilt and die. It is tho
ID: 3128499 • Letter: T
Question
The pathogen Phyotphthora capsici causes bell peppers to wilt and die. It is thought that too much water supports the spread of the pathogen. Two fields are under study. The first step is to compare the mean soil water content(measured in grams of water per 100 grams of soil)in the two fields. The researcher wish to determine whether the mean water content is higher on average in Fields A than it is in Field B. State the null hypothesis and the alternative hypothesis. Use an independent samples t test with alpha=0.05 to determine if there is convincing evidence that Field A has a higher water content than Field B, and state your conclusion.Explanation / Answer
a)
Let u1 = mean of field A
u2 = mean of field B
Formulating the null and alternative hypotheses,
Ho: u1 - u2 <= 0
Ha: u1 - u2 > 0
b)
At level of significance = 0.05
As we can see, this is a right tailed test.
Calculating the means of each group,
X1 = 12.73
X2 = 10.81
Calculating the standard deviations of each group,
s1 = 2.39
s2 = 2.4
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 12
n2 = sample size of group 2 = 14
Hence, df = n1 - 1 = 11
Also, sD = 0.942038696
Thus, the t statistic will be
t = [X1 - X2 - uD]/sD = 2.038132837
where uD = hypothesized difference = 0
Now, the critical value for t is
tcrit = 1.795884819
As t > 1.796, then we Reject Ho.
Hence, there is significant evidence at 0.05 level that Field A has hiher water content than Field B. [CONCLUSION]
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