The pathogen Phytophthora capsici causes bell peppers to wilt and die. Because bell peppers are an important commercial crop, this organism 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 percentage of water by volume of soil.
Field A samples, x1:

Field B samples, x2:

Use a calculator with mean and standard deviation keys to verify that 1 ‰ˆ 12.53, s1 ‰ˆ 2.39, 2 ‰ˆ 10.77, and s2 ‰ˆ 2.40.
(a) Assuming the distribution of soil water content in each field is mound-shaped and symmetrical, use a 5% level of significance to test the claim that field A has, on average, a higher soil water content than field B.
(b) Find a 90% confidence interval for μ1 - μ2. Explain the meaning of the confidence interval in the context of the problem.
Please provide the following information for problem part (a):
(i) What is the level of significance? State the null and alternate hypotheses.
(ii) What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
(iii) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(iv) Based on your answers in parts (i) €“ (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(v) Interpret your conclusion in the context of the application.

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10.2 10.7 15.5 10.4 9.9 10.0 16.6 15.1 15.2 13.8 14.1 11.4 11.5 11.0 8.1 8.5 8.4 7.3 8.07.1 13.9 12.2 13.4 11.3 12.6 12.6 12.4 11.3 12.5