Answered: 1.In a trial for the university…

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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1.In a trial for the university athletics competition, one aims to estimate the mean chest size of the male athletes. A random sample of 70 male athletes gave rise to an average chest size of 42 inches with a standard deviation of 16 inches. What would be the distribution of the statistic that we need to estimate the mean chest size?

a. It is a normal distribution with mean 42 inches and standard deviation 16 inches.

b. it is a student's t distribution with degree of freedom 69.

c. It is a student's t distribution with mean 42 inches and standard deviation 16 inches.

d. it is a normal distribution with degree of freedom 69.

2.What is the standard error of the sample mean in problem 1?

a. 1.91

b. 0.23

c. 17.5

d. 16

3.What would be the critical value if we need to find a 95% confidence interval for the true average chest size in problem 1?

a. 2.29

b. 1.99

c. 1.67

d. None of the above

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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