Answered: The weights of newborn children in the…

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 25:

The weights of newborn children in the United States vary according to the normal distribution with mean 7.5 pounds and standard deviation 1.25 pounds. An article in the The Wall Street Journal claims that the average birth weight is decreasing over time.

A local hospital wanted to see if the claim was true and randomly sampled 23 baby's weights and found an average weight of 7.1 pounds. Test the claim using a 1% level of significance that the mean weight significantly smaller than the national average of 7.5 pounds. Use the population standard deviation of 1.25 pounds. Give answer to at least 4 decimal places.

What are the correct hypotheses? (Select the correct symbols.)

H₀: pounds

H₁: pounds

Based on the hypotheses, find the following:

Test Statistic =

p-value =

The correct decision is to

The correct summary would be: that the mean weight significantly smaller than the national average of 7.5 pounds.

What is the type I error in this situation?

The weights of newborn children in the United States vary according to the normal distribution with mean
7.5 pounds and standard deviation 1.25 pounds. An article in the The Wall Street Journal claims that the
average birth weight is decreasing over time.
Steady Decline
Change in the average birth
weight of babies born in the
U.S. since 1990, in ounces
-0.5
-1.0
-1.5
-2.0
1990 '95 '00
'05
*Born between 37 and 41 weeks and not
including multiple births
Source: Obstetrics and Gynecology
A local hospital wanted to see if the claim was true and randomly sampled 23 baby's weights and found an
average weight of 7.1 pounds. Test the claim using a 1% level of significance that the mean weight
significantly smaller than the national average of 7.5 pounds. Use the population standard deviation of 1.25
pounds. Give answer to at least 4 decimal places.
What are the correct hypotheses? (Select the correct symbols.)
Ho: Select an answer
?
pounds
H₁: Select an answer
pounds
Based on the hypotheses, find the following:
Test Statistic =
p-value =
The correct decision is to Select an answer
that the mean weight
The correct summary would be: [Select an answer
significantly smaller than the national average of 7.5 pounds.
What is the type I error in this situation?
Select an answer
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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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