Answered: Refer to the rabbit ear lengths data…

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

Refer to the rabbit ear lengths data set attached to this question. A fellow researcher believes that the mean ear length of all Mountain cottontail rabbits is 5.7 cm. You believe that it may be smaller than this.

(a) State the null hypothesis and alternative hypothesis. Be sure to define in words the meaning of the parameter “μ,” in the context of this problem.

(b) By hand, carry out a test of significance, to test the researcher’s claim. Show your work at each step.

(c) Was your result in part (b) statistically significant, or not statistically significant? Explain what this result means, using words that would be understood by someone who had never taken a Statistics course.

Rabbit #
Ear length (cm)
1
2
5.4 5.5
3
6.0
4
5.6
5
4.9
6
7
8
5.0 5.1 5.9
9
6.2
10
5.5

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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