Answered: If the sample size is n=81, find the…

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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Question

Q scores are normally distributed with a mean of 95 and a standard deviation of 18. Assume that many samples of size n are taken from a large population of people and the mean IQ score is computed for each sample.

a. If the sample size is n=81, find the mean and standard deviation of the distribution of sample means.

The mean of the distribution of sample is __

The standard deviation of the distribution of sample means is__ (type an integer or decimal rounded to the nearest tenth as needed)

b. If the sample size is n=169, find the mean and standard deviation of the distribution of sample means.

The mean of distribution of sample means is __

The standard deviation of the distribution of sample means is __ (type an iteger or decimal rounded to the nearest tenth as needed)

c. Why is the standard deviation in part A. different from the standard deviation in part B? Choose the correct answer below

A. With smaller sample sizes (as in part a), the means tend to be further apart, so they have more variation, which results in a smaller standard deviation.

B. With larger sample sizes (as in part b) the means tend to be closer together, so they have less variation, which results in a smaller standard deviation.

C. With larger samples (as in part b) the means tend to be further apart, so they have more variation, which results in a bigger standard deviation.

D. With smaller sample sizes (as in part a) the means tend to be closer together, so they have less variation, which results in a smaller standard deviation.

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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