Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 12.2, Problem 24E
The invasive diatom species Didymosphenia geminata has the potential to inflict substantial ecological and economic damage in rivers. The article “Substrate Characteristics Affect Colonization by the Bloom-Forming Diatom Didymosphenia geminata (Aquatic Ecology, 2010: 33–40) described an investigation of colonization behavior. One aspect of particular interest was whether y = colony density was related to x = rock surface area. The article contained a
| x | 50 | 71 | 55 | 50 | 33 | 58 | 79 | 26 |
| y | 152 | 1929 | 48 | 22 | 2 | 5 | 35 | 7 |
| x | 69 | 44 | 37 | 70 | 20 | 45 | 49 |
| y | 269 | 38 | 171 | 13 | 43 | 185 | 25 |
- a. Fit the simple linear regression model to this data, predict colony density when surface area = 70 and when surface area = 71, and calculate the corresponding residuals. How do they compare?
- b. Calculate and interpret the coefficient of determination.
- c. The second observation has a very extreme y value (in the full data set consisting of 72 observations, there were two of these). This observation may have had a substantial impact on the fit of the model and subsequent conclusions. Eliminate it and recalculate the equation of the estimated regression line. Does it appear to differ substantially from the equation before the deletion? What is the impact on r2 and s?
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Tardigrades, or water bears, are a type of micro-animal famous for their resilience. In examining the effects of radiation on organisms, an expert claimed that the amount of gamma radiation needed to sterilize a colony of tardigrades no longer has a mean of
900
Gy
(grays). (For comparison, humans cannot withstand more than
10
Gy
.) A study was conducted on a sample of
27
randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of
907
Gy
, with a sample standard deviation of
17
Gy
. Assume that the population of amounts of gamma radiation needed to sterilize a colony of tardigrades is approximately normally distributed.
Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the
0.05
level of significance, to support the claim that
μ
, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to
900…
Tardigrades, or water bears, are a type of micro-animal famous for their resilience. In examining the effects of radiation on organisms, an expert claimed that the amount of gamma radiation needed to sterilize a colony of tardigrades no longer has a mean of
900
Gy
(grays). (For comparison, humans cannot withstand more than
10
Gy
.) A study was conducted on a sample of
27
randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of
907
Gy
, with a sample standard deviation of
17
Gy
. Assume that the population of amounts of gamma radiation needed to sterilize a colony of tardigrades is approximately normally distributed.
Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the
0.05
level of significance, to support the claim that
μ
, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to
900…
The article “Effects of Diets with Whole Plant-Origin Proteins Added with Different Ratiosof Taurine:Methionine on the Growth, Macrophage Activity and Antioxidant Capacity ofRainbow Trout (Oncorhynchus mykiss) Fingerlings” (O. Hernandez, L. Hernandez, et al.,Veterinary and Animal Science, 2017:4-9) reports that a sample of 210 juvenile rainbowtrout fed a diet fortified with equal amounts of the amino acids taurine and methionine for aperiod of 70 days had a mean weight gain of 313 percent with a standard deviation of 25, while 210 fish fed with a control diet had a mean weight gain of 233 percent with a standard deviation of 19. Units are percent. Find a 99% confidence interval for the difference in weight gain on the two diets.
Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
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