Tracking the mean age of a first-time mother is of interest to researchers and the public since it can affect the total number of births a mother has in a lifetime, which in turn impacts the composition and growth of the US population. Back in 2016, the mean age of first-time mothers was 26.3 years. Researchers surveyed 952 US mothers and found that the mean first-time mother age is 28.2 years with a standard deviation of 1.03 years. Test the claim that the mean age of first-time mothers has not changed from 26.3 years. Assume the significance level is 0.01. The test ouptut is below: State the conclusion of this test. a. There is sufficient evidence that the mean age of first-time mothers has decreased from 26.3 years. b. There is sufficient evidence that the mean age of first-time mothers is different from 26.3 years. c. There is sufficient evidence that the mean age of first-time mothers has increased from 26.3 years. d. There is not sufficient evidence that the mean age of first-time mothers is different from 26.3 years. Interpret the p-value. a. There is a probability of less than 0.0001 that the mean age of first-time mothers is equal to 26.3. b. If the mean age of first-time mothers is greater than 26.3, then the probability of getting a sample mean of 28.2 or something more extreme is less than 0.0001. c. If the mean age of first-time mothers is equal to 26.3, then the probability of getting a sample mean of 28.2 or something more extreme is less than 0.0001. d. If the mean age of first-time mothers is less than 26.3, then the probability of getting a sample mean of 28.2 or something more extreme is less than 0.0001.

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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Tracking the mean age of a first-time mother is of interest to researchers and the public since it can affect the total number of births a mother has in a lifetime, which in turn impacts the composition and growth of the US population. Back in 2016, the mean age of first-time mothers was 26.3 years. Researchers surveyed 952 US mothers and found that the mean first-time mother age is 28.2 years with a standard deviation of 1.03 years. Test the claim that the mean age of first-time mothers has not changed from 26.3 years. Assume the significance level is 0.01. The test ouptut is below:

State the conclusion of this test.

	a.	There is sufficient evidence that the mean age of first-time mothers has decreased from 26.3 years.
	b.	There is sufficient evidence that the mean age of first-time mothers is different from 26.3 years.
	c.	There is sufficient evidence that the mean age of first-time mothers has increased from 26.3 years.
	d.	There is not sufficient evidence that the mean age of first-time mothers is different from 26.3 years.

Interpret the p-value.

	a.	There is a probability of less than 0.0001 that the mean age of first-time mothers is equal to 26.3.
	b.	If the mean age of first-time mothers is greater than 26.3, then the probability of getting a sample mean of 28.2 or something more extreme is less than 0.0001.
	c.	If the mean age of first-time mothers is equal to 26.3, then the probability of getting a sample mean of 28.2 or something more extreme is less than 0.0001.
	d.	If the mean age of first-time mothers is less than 26.3, then the probability of getting a sample mean of 28.2 or something more extreme is less than 0.0001.

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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