Question

Phosphorous is a chemical that is found in many household cleaning products. Unfortunately, phosphorous also finds its way into surface water, where it can harm fish, plants, and other wildlife. Two methods of phosphorous reduction are being studied. At a random sample of 7 locations, both methods were used and the total phosphorous reduction (mg/L) was recorded. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. Site 1 2 3 4 5 6 7 Method I: 0.013 0.020 0.015 0.055 0.007 0.002 0.010 Method II: 0.014 0.045 0.017 0.039 0.017 0.001 0.013 Do these data indicate a difference (either way) in the average reduction of phosphorous between the two methods? Use α = 0.05. (Let d = Method I − Method II.) (i) What is the level of significance? State the null and alternate hypotheses. H0: μd > 0; H1: μd = 0 H0: μd = 0; H1: μd ≠ 0 H0: μd = 0; H1: μd > 0 H0: μd = 0; H1: μd < 0 (ii) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that d has an approximately normal distribution. The standard normal. We assume that d has an approximately uniform distribution. The Student's t. We assume that d has an approximately normal distribution. The Student's t. We assume that d has an approximately uniform distribution. What is the value of the sample test statistic? (Round your answer to three decimal places.) (iii) Find (or estimate) the P-value. P-value > 0.500 0.250 < P-value < 0.500 0.100 < P-value < 0.250 0.050 < P-value < 0.100 0.010 < P-value < 0.050 P-value < 0.010 Sketch the sampling distribution and show the area corresponding to the P-value. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (iv) Based on your answers in parts (i) to (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 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. There is sufficient evidence at the 0.05 level to conclude that there is a difference in phosphorous reduction between the two methods. There is insufficient evidence at the 0.05 level to conclude that there is a difference in phosphorous reduction between the two methods.

Answer 1

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

V)

There is insufficient evidence at the 0.05 level to conclude that there is a difference in phosphorous reduction between the two methods.