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: x1; n = 15 855 1550 1230 875 1080 2330 1850 1860 2340 1080 910 1130 1450 1260 1010 Region II: x2; n2 = 14 540 810 790 1230 1770 960 1650 860 890 640 1180 1160 1050 1020 (a) Use a calculator with mean and standard deviation keys to verify that x1, $1, X2, and s2. (Round your answers to one decimal place.) X1 = ppm S1 = ppm ppm ppm X2 = S2 = (b) Let µ1 be the population mean for x1 and let 42 be the population mean for x2. Find a 95% confidence interval for 41 - 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 95% 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. 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. 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'st was used because o, and oz are known. Student's t was used because og and az are unknown. O Standard normal was used because o, and oz are unknown. Standard normal was used because o and oz are known.
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: x1; n = 15 855 1550 1230 875 1080 2330 1850 1860 2340 1080 910 1130 1450 1260 1010 Region II: x2; n2 = 14 540 810 790 1230 1770 960 1650 860 890 640 1180 1160 1050 1020 (a) Use a calculator with mean and standard deviation keys to verify that x1, $1, X2, and s2. (Round your answers to one decimal place.) X1 = ppm S1 = ppm ppm ppm X2 = S2 = (b) Let µ1 be the population mean for x1 and let 42 be the population mean for x2. Find a 95% confidence interval for 41 - 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 95% 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. 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. 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'st was used because o, and oz are known. Student's t was used because og and az are unknown. O Standard normal was used because o, and oz are unknown. Standard normal was used because o and oz are known.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Inorganic Phosphorous in Plants and Animals: A Geochemical Survey**
Inorganic phosphorous is a naturally occurring element in all plants and animals, with its 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: \( x_{1i} \, n_1 = 15 \)**
- 855, 1550, 1230, 875, 1080, 2330, 1850, 1860
- 2340, 1080, 910, 1130, 1450, 1260, 1010
**Region II: \( x_{2i} \, n_2 = 14 \)**
- 540, 810, 790, 1230, 1770, 960, 1650, 860
- 890, 640, 1180, 1160, 1050, 1020
**Tasks:**
(a) **Use a calculator with mean and standard deviation keys to verify the following values:** (Round your answers to one decimal place.)
- \(\bar{x}_1 = \) _____ ppm
- \(s_1 = \) _____ ppm
- \(\bar{x}_2 = \) _____ ppm
- \(s_2 = \) _____ ppm
(b) **Find a 95% confidence interval for \( \mu_1 - \mu_2 \):** (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 95% level of confidence, is one region more interesting than the other from a geochemical perspective?**
- Because the interval contains both positive and negative numbers, we cannot say that one region is more interesting than the other.
- Because the interval contains only positive numbers, we can say that
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