A clinical trial is being conducted in order to determine the efficacy of a new drug that will be used to treat Crohn’s disease. The efficacy of the medication will not only be determined by the physical improvement of symptoms but will also be determined by using a blood test to examine the concentration of C-reactive protein (an inflammatory marker) in an individual’s blood. If the researcher wants the margin of error for the level of C-reactive protein to be less than or equal to 2.9 mg/dL and the standard deviation for C-reactive protein concentrations among Crohn’s disease patients was previously documented at 10.1 mg/dL, how many patients should be recruited for each group of individuals in the study, assuming a 95% confidence interval will be used to quantify the mean differences between the control group and the treatment group? n for the treatment group = 12 and n for the control group = 12 n for the treatment group = 14 and n for the control group = 14 n for the treatment group = 47 and n for the control group = 47 n for the treatment group = 94 and n for the control group = 94 --------I'm confused which formula to use-------- For 95% confidence, z = 1.96, Standard deviation = 10.1, E = 2.9 Sample size: n = ((1.96 x 10.1) / 2.9)² = 47 ------OR------- For 95% CI crtiical Z = 1.96 first sample standard deviation σ1 = 10.1 second sample standard deviation σ2 = 10.1 margin of error E = 2.9 required sample size n = (z/E)²(σ1²+σ2²) = 94

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Description: A clinical trial is being conducted in order to determine the efficacy of a new drug that will be used to treat Crohn’s disease. The efficacy of the medication will not only be determined by the physical improvement of symptoms but will also be deter

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 2AGP

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A clinical trial is being conducted in order to determine the efficacy of a new drug that will be used to treat Crohn’s disease. The efficacy of the medication will not only be determined by the physical improvement of symptoms but will also be determined by using a blood test to examine the concentration of C-reactive protein (an inflammatory marker) in an individual’s blood. If the researcher wants the margin of error for the level of C-reactive protein to be less than or equal to 2.9 mg/dL and the standard deviation for C-reactive protein concentrations among Crohn’s disease patients was previously documented at 10.1 mg/dL, how many patients should be recruited for each group of individuals in the study, assuming a 95% confidence interval will be used to quantify the mean differences between the control group and the treatment group?

n for the treatment group = 12 and n for the control group = 12

n for the treatment group = 14 and n for the control group = 14

n for the treatment group = 47 and n for the control group = 47

n for the treatment group = 94 and n for the control group = 94

--------I'm confused which formula to use--------

For 95% confidence, z = 1.96, Standard deviation = 10.1, E = 2.9

Sample size:

n = ((1.96 x 10.1) / 2.9)² = 47

------OR-------

For 95% CI crtiical Z = 1.96

first sample standard deviation σ1 = 10.1

second sample standard deviation σ2 = 10.1

margin of error E = 2.9

required sample size n = (z/E)²(σ1²+σ2²) = 94

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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