Answered: #7. A psychologist is studying the self…

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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#7. A psychologist is studying the self image of smokers, which she measures by the self image (SI) score from a personality inventory. She would like to estimate the mean SI score, U (population mean), for the population of all smokers. She plans to take a random sample of SI scores for the smokers and estimate U (population mean) via this sample. Assuming that the standard deviation of us are scores for the population of all smokers is 82, what is the minimum sample size needed for the psychologist to be 99% confident that her estimate is within 10 of U (population mean)? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number and make sure that it is the minimum whole number necessary that satisfies the requirements.

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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