Samples of head breadths were obtained by measuring skulls of Egyptian males from three different epochs, and the measurements are listed below. Changes in head shape over time suggest that interbreeding occurred with immigrant populations. Use a 0.05 significance level to test the claim that the different epochs have the same mean. 4000 BC: 131 138 125 129 132 135 132 134 138 1850 BC: 129 134 136 137 137 129 136 138 134 150 AD: 128 138 136 139 141 142 137 145 137 a. Define the parameter(s) A. mu equals The mean head breadth of Egyptian males B. mu equals The mean change in head shape C. mu 1 equals The mean head breadth from 4000 BC mu 2 equals The mean head breadth from 1850 BC mu 3 equals The mean head breadth from 150 AD D. p 1 equals The mean head breadth from 4000 BC p 2 equals The mean head breadth from 1850 BC p 3 equals The mean head breadth from 150 AD b. State Upper H 0 . A. mu 1 not equals mu 2 not equals mu 3 B. mu greater than 0 C. mu 1 equals mu 2 equals mu 3 equals 3.5 D. mu 1 equals mu 2 equals mu 3 c. Calculate the P-value. Which of these options is closest to the P-value? A. 0.0207 B. 0.0317 C. 0.0305 D. 0.0196

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Description: Samples of head breadths were obtained by measuring skulls of Egyptian males from three different epochs, and the measurements are listed below. Changes in head shape over time suggest that interbreeding occurred with immigrant populations. Use a 0.

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Samples of head breadths were obtained by measuring skulls of Egyptian males from three different epochs, and the measurements are listed below. Changes in head shape over time suggest that interbreeding occurred with immigrant populations. Use a 0.05 significance level to test the claim that the different epochs have the same mean.

4000 BC: 131 138 125 129 132 135 132 134 138

1850 BC: 129 134

136

137 137 129 136 138 134

150 AD: 128 138 136 139 141 142 137 145 137

a. Define the parameter(s)

mu equals

The

mean head breadth of Egyptian males

mu equals

The

mean change in head shape

mu 1 equals

The

mean head breadth from 4000 BC

mu 2 equals

The

mean head breadth from 1850 BC

mu 3 equals

The

mean head breadth from 150 AD

p 1 equals

The

mean head breadth from 4000 BC

p 2 equals

The

mean head breadth from 1850 BC

p 3 equals

The

mean head breadth from 150 AD

b. State

Upper H 0

mu 1 not equals mu 2 not equals mu 3

mu greater than 0

mu 1 equals mu 2 equals mu 3 equals 3.5

mu 1 equals mu 2 equals mu 3

c. Calculate the P-value. Which of these options is closest to the P-value?

0.0207

0.0317

0.0305

0.0196

d. State the technical conclusion.

Reject Upper H 0

Do not reject Upper H 0

e. State the final conclusion.

There is sufficient evidence to warrant rejection of the claim.

There is not sufficient evidence to warrant rejection of the claim.

There is not sufficient sample evidence to support the claim.

The sample data support the claim.

f. Does it appear that the skull breadths have changed over time?

Yes

g. Does this suggest that interbreeding has occurred?

Yes

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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