Answered: In a randomized double-blind,…

Name: In a randomized double-blind, placebo-controlled trial of children,
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Description: In a randomized double-blind, placebo-controlled trial of children, an herb was tested as a treatment for upper respiratory infections in children. "Days of fever" was one criterion used to measure effects. Among 333 children treated with the he

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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In a randomized double-blind, placebo-controlled trial of children, an herb was tested as a treatment for upper respiratory infections in children. "Days of fever" was one criterion used to measure effects. Among 333 children treated with the herb, the mean number of days with fever was 0.89, with a standard deviation of 1.51 days. Among 379 children given a placebo, the mean number of days with fever was 0.68 with a standard deviation of 1.06 days. Use a 0.01 significance level to test the claim that the herb affects the number of days with fever. Based on these results, does the herb appear to be effective? Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Let population 1 be children treated with the herb.

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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