Answered: A student claims that professional male…

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

A student claims that professional male basketball players are taller, on average, than college male basketball players. To investigate this claim, the student selects a random sample of 30 professional basketball players and 30 college basketball players. The mean height of the sample of professional male basketball players is 76 inches with a standard deviation of 3.5 inches. The mean height of the sample of college male basketball players is 74.5 inches with a standard deviation of 5.5 inches. The student would like to determine if there is convincing evidence that the true mean height of all professional male basketball players is greater than the true mean height of all college male basketball players. The hypotheses H₀: μ₁ – μ₂ = 0, H_a: μ₁ – μ₂ > 0 are tested where μ₁ = the true mean height of all professional male basketball players, and μ₂ = the true mean height of all college male basketball players. The conditions for inference have been met. What are the values of the test statistic and P-value for a t-test about a difference in means?

Find the t-table here and the z-table here.

t = –1.26. The P-value is between 0.10 and 0.15.

z = –1.26. The P-value is 0.1038.

t = 1.26. The P-value is between 0.10 and 0.15.

z = 1.26. The P-value is 0.1038.

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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