Example 1: Recent research suggests that a pregnancy within less than two years of a live birth might be associated with an increased risk of autism in second-born children. Below is a data set containing the ages of 15 siblings. Does the sample indicate that couples are waiting more than two years before getting pregnant with a second child? (Note that the average length of human gestation is 40 weeks which is approximately 0.77 years). Since this data is paired (and clearly not independent), we do not use the 2-Sample T-Interval or 2-Sample T-Test. Instead, we consider the pairwise differences. Using our calculator, enter the age of the first child into L1 and the age of the second child into L2. Move your cursor over L3 and enter L1-L2. Press Enter. L3 will fill with the pairwise differences. a) Conduct a t-Test to determine if couples are waiting more than two years before getting pregnant with a second child. Be sure to write the name of the test, state the hypotheses, find the p-value and test statistic, and state your conclusion. Use a significance level of 0.10. Paired t-Test Ho: Md = 2.77 На: мы 7 2.77 L1 First Child 7.08 5.29 2.75 5.92 4.23 4.17 3.13 6.31 5.38 4.67 8.57 6.28 2.92 4.38 5.5 L2 L3=11-L2 Second Child 3.5 3.81 0.83 2.79 3.02 1.38 1.55 1.92 2.81 3.15 4.23 3.67 0.56 1.15 2.23 Pairwise Difference 3.58 1.48 1.92 3.13 1.21 2.79 1.58 4.39 2.57 1.52 4.34 2.61 2.34 3.23 3.27

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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Please explain how they recieced 2.77 as the mean difference. Please step by step

Example 1: Recent research suggests that a pregnancy within less than two years of a live birth might be
associated with an increased risk of autism in second-born children. Below is a data set containing the
ages of 15 siblings. Does the sample indicate that couples are waiting more than two years before getting
pregnant with a second child? (Note that the average length of human gestation is 40 weeks which is
approximately 0.77 years).
Since this data is paired (and clearly not independent), we do not
use the 2-Sample T-Interval or 2-Sample T-Test. Instead, we
consider the pairwise differences.
Using our calculator, enter the age of the first child into L1 and the
age of the second child into L2. Move your cursor over L3 and enter
L1 L2. Press Enter. L3 will fill with the pairwise differences.
a) Conduct a t-Test to determine if couples are waiting more
than two years before getting pregnant with a second child.
Be sure to write the name of the test, state the hypotheses,
find the p-value and test statistic, and state your conclusion.
Use a significance level of 0.10.
Paired t-Test
Ho: Md = 2.77
HA: Md > 2.77
L1
First
Child
7.08
5.29
2.75
5.92
4.23
4.17
3.13
6.31
5.38
4.67
8.57
6.28
2.92
4.38
5.5
L2 L3=11-12
Second
Pairwise
Child
Difference
3.5
3.81
0.83
2.79
3.02
1.38
1.55
1.92
2.81
3.15
4.23
3.67
0.56
1.15
2.23
3.58
1.48
1.92
3.13
1.21
2.79
1.58
4.39
2.57
1.52
4.34
2.61
2.34
3.23
3.27
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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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