Answered: Researchers are studying the effect of…

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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Researchers are studying the effect of smoking on the time it takes to fall asleep. A random sample of 50 smokers reported a mean time until sleep of 43.3 minutes with a standard deviation of 12.4 minutes. A random sample of 75 nonsmokers reported a mean time until sleep of 30.2 minutes with a standard deviation of 9.1 minutes. Construct a two-sided 95% confidence interval for the difference between the two means. Assume equal variances. 1. The value for t and how you found it 2. The calculation of the pooled variance (3. The calculation of the Standard Error, 4. The calculation of the Margin of Error, 5. The calculation of the upper and lower limits, and 6. An interpretation that includes whether the means differ

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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