The pathogenPhytophthora capsicicauses 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 percentage of water by volume of soil.

Field A samples,x₁:10.0, 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

Use a calculator to calculatex₁,s₁,x₂, ands₂. (Round your answers to four decimal places.)

• x₁=
• s₁=
• x₂=
• s₂=

(a)Assuming the distribution of soil water content in each field is mound-shaped and symmetric, use a5% levelof significance to test the claim thatfield Ahas, on average, a higher soil water content thanfield B.

(i)What is the level of significance?

State the null and alternate hypotheses.

• H₀:₁=₂;H₁:₁<₂
• H₀:₁=₂;H₁:₁>₂
• H₀:₁>₂;H₁:₁=₂
• H₀:₁=₂;H₁:₁₂

(ii)What sampling distribution will you use? What assumptions are you making?

• The Student'st. We assume that both population distributions are approximately normal with unknown standard deviations.
• The Student'st. We assume that both population distributions are approximately normal with known standard deviations.
• The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
• The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.

What is the value of the sample test statistic? Compute the correspondingzort-value as appropriate. (Test the difference₁₂.Do not use rounded values. Round your final answer to three decimal places.)

(iii)Find (or estimate) theP-value.

• P-value > 0.250
• 0.125 <P-value < 0.250
• 0.050 <P-value < 0.125
• 0.025 <P-value < 0.050
• 0.005 <P-value < 0.025
• P-value < 0.005

Sketch the sampling distribution and show the area corresponding to theP-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?

• At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
• At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
• At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
• At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(v)Interpret your conclusion in the context of the application.

• Reject the null hypothesis, there is sufficient evidence that mean soil water content is higher in Field A.
• Fail to reject the null hypothesis, there is insufficient evidence that mean soil water content is higher in Field A.
• Reject the null hypothesis, there is insufficient evidence that mean soil water content is higher in Field A.
• Fail to reject the null hypothesis, there is sufficient evidence that mean soil water content is higher in Field A.

(b)Find a 90% confidence interval for₁₂.

(Round your answers to two decimal places.)

• lower limit=
• upper limit=

(c) Explain the meaning of the confidence interval in the context of the problem.

• Because the interval contains only positive numbers, this indicates that at the 90% confidence level, the mean soil water content forField Ais higher than that ofField B.
• Because the interval contains both positive and negative numbers, this indicates that at the 90% confidence level, we cannot say that the mean soil water content forField Ais higher than that ofField B.
• Because the interval contains both positive and negative numbers, this indicates that at the 90% confidence level, the mean soil water content forField Ais lower than that ofField B.
• Because the interval contains only negative numbers, this indicates that at the 90% confidence level, the mean soil water content forField Ais lower than that ofField B.