What is the impact of caffeine on performance in endurance cycling races? Thirty subjects were divided into 10 groups, and each group was given one of three doses of caffeine (0, 3, 6 mg/kg) in a drink, and the time to cycle the equivalent of 40 km on a stationary bicycle was recorded. Here is an (incomplete) diagram of the experiment. (e) Random Assignment (a) (c) (h) (d) (g) Which of the following is correct in completing the figure? O (b), (c), and (d) are subjects. O (a) are subjects. O (e), (f), and (g) are the doses of caffeine. O (h) is where the doses of caffeine are compared.

(iii) Find (or estimate) the P-value. OP-value > 0.250 O 0.125 < P-value < 0.250 O 0.050 < P-value < 0.125 O 0.025 < P-value < 0.050 O 0.005< P-value < 0.025 OP-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. O -4 -2 0 2 2 M 2 DO Q -2 -2 (iv) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. O At the a= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. (v) Interpret your conclusion in the context of the application. O Fail to reject the null hypothesis, there…

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. Things that are labelled i underneath a b c, etc are all part of that part.

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?   What is the value of the sample test statistic? (Round…