Answered: The accompanying table lists heights…

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

The accompanying table lists heights (in inches) of randomly selected fathers and their first sons. Use a 0.05 significance level to test the claim that there is no difference in heights between fathers and their first sons.

H
e
i
g
h
t
o
f
F
a
t
h
e
r
H
e
i
g
h
t
o
f
S
o
n
6
9.4
6
8.0
7
1.4
7
1.3
6
8.8
7
0.5
6
9.0
7
1.5
7
1.0
7
2.9
6
5.3
6
7.7
6
7.2
6
4.6
7
0.3
7
0.2
6
6.9
6
9.5
6
8.2
7
1.3
6
1.5
6
4.9
6
8.6
6
9.9
6
9.5
7
1.3
7
4.0
7
4.8
7
1.3
6
7.9
6
8.1
7
0.8
7
2.7
7
3.4
7
1.8
7
3.5
7
3.8
7
3.2
7
1.1
7
7.4
7
1.5
7
3.4
6
9.8
6
7.1
6
9.6
6
7.5
6
9.3
6
8.6
6
7.1
6
7.9
6
6.0
6
6.9
6
9.5
7
0.7
6
8.0
7
0.9
6
6.1
7
0.0
6
5.1
6
5.2
6
8.8
6
5.6
7
2.0
7
1.6
7
2.1
6
9.5
6
8.7
7
0.7
6
5.2
6
7.0
7
1.8
7
1.9
7
1.5
7
4.1
7
2.2
7
2.5
7
0.5
7
3.8
7
0.7
6
9.4
6
8.5
6
5.4
6
7.4
6
9.8
7
1.3
7
3.8
6
9.1
7
1.6
6
9.0
7
2.1
7
0.0
6
9.5
7
3.0
7
1.1
6
9.1
6
9.5
6
9.5
7
0.4
6
9.1
7
3.2
6
7.3
6
9.1
6
8.7
7
2.4
6
7.3
6
8.7
6
9.2
6
9.0
7
6
2
7
3
2
10/30/21, 12:18 AM Heights
https://www.mathxl.com/Student/PlayerTest.aspx?testId=230138677 2/2
76.2 73.2
65.4 69.9
69.1 78.1
70.5 72.4
68.3 72.2
68.5 71.1
69.3 71.8
64.2 65.1
68.4 69.7
68.3 71.0
70.7 69.6
67.2 71.6
71.7 72.0
65.3 69.7
66.1 70.6
65.4 71.3
70.7 69.8
66.9 69.7
70.1 70.3
64.9 70.1
64.0 70.3

In this example,

μd

is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the height of the father minus the height of the first son. What are the null and alternative hypotheses for the hypothesis test?

H0:

μd

▼

not equals≠

less than<

equals=

greater than>

enter your response here

in.

H1:

μd

▼

not equals≠

greater than>

equals=

less than<

enter your response here

in.

(Type integers or decimals. Do not round.)

Identify the test statistic.

t=enter your response here

(Round to two decimal places as needed.)

Identify the P-value.

P-value=enter your response here

(Round to three decimal places as needed.)

What is the conclusion based on the hypothesis test?

Since the P-value is

▼

less

greater

than the significance level,

▼

fail to reject

reject

H0.

There

▼

is not

sufficient evidence to warrant rejection of the claim of no difference in heights between fathers and their first sons.

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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