The ability to release antibiotics locally in traumatic bone injuries such as those experienced by military personnel in combat has been shown to be effective at reducing the number of infectious complications, reducing the number of amputations and increasing recovery rates. Calcium sulfate has been shown to be an effective local delivery carrier for the antibiotic, daptomycin. One goal has been to extend the the amount of daptomycin released into saline from calcium sulfate pellets coated or uncoated with chitosan.  Release of daptomycin (μg/mL) from calcium sulfate coated with chitosan: 137.61, 156.52, 185.82, 158.67, 164.31, 186.55, 200.81, 191.63, 173.39, 140.43, 167.11, 192.73, 157.34, 152.58, 177.69 Release of daptomycin (μg/mL) from calcium sulfate uncoated: 148.10, 127.28, 136.51, 134.71, 159.41, 128.54, 148.22, 141.89, 156.87, 151.66, 143.88, 153.17, 148.42, 142.44, 158.80 Conduct the appropriate two sample t-test at the α = 0.05 level of significance to determine if there is any effect of the chitosan coating on the release of the antibiotics from the calcium sulfate. a. State your H0 and Ha and if this is 1-tailed or 2-tailed b. What assumptions do you make regarding distribution of the data? how do you verify? c. Perform appropriate two sample t-test ( unequal) d. State p-value from t-tests and conclusion . e. Calculate 95% CI for the difference of the means of the two groups and state conclusion.

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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The ability to release antibiotics locally in traumatic bone injuries such as those experienced by military personnel in combat has been shown to be effective at reducing the number of infectious complications, reducing the number of amputations and increasing recovery rates. Calcium sulfate has been shown to be an effective local delivery carrier for the antibiotic, daptomycin. One goal has been to extend the the amount of daptomycin released into saline from calcium sulfate pellets coated or uncoated with chitosan. 

Release of daptomycin (μg/mL) from calcium sulfate coated with chitosan: 137.61, 156.52, 185.82, 158.67, 164.31, 186.55, 200.81, 191.63, 173.39, 140.43, 167.11, 192.73, 157.34, 152.58, 177.69

Release of daptomycin (μg/mL) from calcium sulfate uncoated: 148.10, 127.28, 136.51, 134.71, 159.41, 128.54, 148.22, 141.89, 156.87, 151.66, 143.88, 153.17, 148.42, 142.44, 158.80

Conduct the appropriate two sample t-test at the α = 0.05 level of significance to determine if there is any effect of the chitosan coating on the release of the antibiotics from the calcium sulfate.

a. State your H0 and Ha and if this is 1-tailed or 2-tailed

b. What assumptions do you make regarding distribution of the data? how do you verify?

c. Perform appropriate two sample t-test ( unequal)

d. State p-value from t-tests and conclusion .

e. Calculate 95% CI for the difference of the means of the two groups and state conclusion.

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