Inorganic phosphorous is a naturally occurring element in all plants and animals, with concentrations increasing progressively up the food chain (fruit < vegetables < cereals < nuts < corpse). Geochemical surveys take soil samples to determine phosphorous content (in ppm, parts per million). A high phosphorous content may or may not indicate an ancient burial site, food storage site, or even a garbage dump. Independent random samples from two regions gave the following phosphorous measurements (in ppm). Assume the distribution of phosphorous is mound-shaped and symmetric for these two regions. Region I: x,; n, = 15 857 1,553 1,230 875 1,080 2,330 1,850 1,860 2,340 1,080 910 1,130 1,450 1,260 1,010 Region II: x2; n2 = 14 538 810 790 1,230 1,770 960 1,650 860 890 640 1,180 1,160 1,050 1,020 A USE SALT (a) Use a calculator with mean and standard deviation keys to verify that x,, s,, X2, and s,. (Round your answers to four 14 decimal places.) X, = ppm S, = ppm X2 ppm S2 ppm %3D (b) Let u, be the population mean for x, and let µ, be the population mean for x,. Find an 80% confidence interval for H1 - H2. (Round your answers to one decimal place.) lower limit ppm upper limit ppm (c) Explain what the confidence interval means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 80% level of confidence, is one region more interesting than the other from a geochemical perspective? O Because the interval contains both positive and negative numbers, we can not say that one region is more interesting than the other. O Because the interval contains only positive numbers, we can say that region I is more interesting than region II. O Because the interval contains only negative numbers, we can say that region II is more interesting than region I. O We can not make any conclusions using this confidence interval. (d) Which distribution (standard normal or Student's t) did you use? Why? O Student's t was used because o, and o, are unknown. O Standard normal was used because o, and 0, are known. O Standard normal was used because o, and o, are unknown. O Student'st was used because o, and o, are known.

An article in Lubrication Engineering (December 1990) described the results of an experiment designed to investigate the effects of carbon material properties on the progression of blisters on carbon face seals. The carbon face seals are used extensively in equipment such as air turbine starters. Four different carbon materials were tested, and the surface roughness was measured. The data are as follows: Carbon Material Type Surface Roughness EC 10 0.50 0.55 0.55 0.36     EC10A 0.31 0.07 0.25 0.18 0.56 0.20 EC4 0.20 0.28 0.12       EC1 0.10 0.16         Does carbon material type have an effect on mean surface roughness? Use α = 0.05.

The toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. Here are data for beak heat loss, as a percent of total body heat loss from all sources, at various temperatures in degrees Celsius. [Note: The numerical values in this problem have been modified for testing purposes.] Temperature (oC)(oC) 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Percent heat loss from beak 33 33 34 31 37 46 54 49 41 50 44 56 55 61 64 59 The equation of the least-squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature is: (Use decimal notation. Enter the values of the intercept and slope rounded to two decimal…

QUESTION 10 An experiment was run to determine whether four specific firing temperatures affect the density of a certain type of brick. A completely randomized experiment was conducted with 4 replications and led to a MSE= 50.65. Use a=0.05. Calculate the Tukey's significant difference value to compare two means.