Table 14.1 54 54 56 58 58 59 60 60 60 60 60 60 60 60 61 61 61 61 61 61 61 61 62 62 62 62 62 62 62 62 62 62 62 62 62 62 62 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 65 65 65 65 65 65 65 65 66 66 66 67 67 67 67 68 68 70. 14.46) Table 14.1 provides the heights of a random sample of 93 female undergraduate students at the university of California at Irvine. Assuming that heights in this undergraduate population are normal with standar deviation o= 2.5 inches, do the data provide evidence that the mean height of all female undergraduate students at UC-Irvine is different from the mean height of 64.5 inches of all young women in the United States? Follow the four-step process as ilustatrated in Example 14.9. this setting.quoted value a paper in by CarlSTATE: you the for what or healthyP-value in mind that tables can offer only P-values).cedures, the the area or areas underFahrenheit or 37.0 Celsius, is widelybody you will that an oral of 98.6 degreesprinted such as B or C at back of the book to obtain the testit the use an applet for computations or ade not have access to technology capable of pertorming inference pro-If yo ketch the Normal sampling distribution and the area or areas underno Jprinted keep in mind that printed tables can offer only approximate P-values).Body temperatureEXAMPLE 14.9ATE: When you search the internet for what constitutes "normal" or healthyudy temperature, you will probably find that an oral temperature of 98.6 degreesbrenheit (°F), or 37.0 degrees Celsius, is considered normal. This widelyoted value comes from a paper published in 1868 by German physician CarlWanderlich, in which he reported more than a million body temperature read-s In this paper, Wunderlich stated that the mean body temperature of healthyadults is 98.6 °F. More than a century later, a study was designed to evaluate thisclaim. It found a mean oral temperature of x=98.25 °F from 130 adults. Doesthis study provide significant evidence that Wunderlich's claim of a mean adultSTEPрaper,body temperature of 98.6 °F is not correct?PLAN: The null hypothesis is "no difference" from the accepted meanOu,un = 98.6 °F. The alternative is two-sided because the study did not have a%3D particular in mind the data. Thus, the hypothesesSOLVE: Check the for are the conditions"INTRODUCTION TO INFERENCEabout the unknown mean u of the population of healthy adults areHo: u = 98.6= nlHa: µ #98.6SOLVE: Check the conditions for inference. Here are the "simple conditionstated on page 348.1. SRS: The most important condition is that the 130 healthy adults in theple are an SRS from the population of all healthy adults. We should check thi,requirement by asking how the data were obtained. The researchers measuredthe baseline oral temperature of volunteers participating in various vaccineclinical trials conducted at the University of Maryland. If these individualsenrolled in the clinical trial because of a specific medical concern, for exam-ple, the data may not be representative of the whole healthy-adult populationand could be biased. The researchers assure us that the volunteers were allhealthy. Because the subjects were volunteers, the sample is a random samplebut not a true SRS. This is very common in the life sciences, especially whendealing with human subjects.-wes2. Normal distribution: We should examine the distribution of the 130 obser-vations to look for signs that the population distribution is not Normal.A histogram in the published report indicates that the data were roughlyNormal.3. Known o: It is unrealistic to suppose that we know that o = 0.6 °F. Thisvalue is based on Wunderlich's original report of a very large number of body%3Dtemperatures.SOLVE: Obtain the test statistic and P-value. Figure 14.8 shows the output for aone-sample z test using statistical software JMP. It gives z= -6.651 and a Pvalerounded to zero, based on which the output specifies that we should "reject thenull hypothesis."CONCLUDE: If u really was 98.6 °F, it would be nearly impossible to obta osobtain anSRS of size 130 from the healthy adult population with sample mean at forevery strong evidence that the true mean body temperature of healthy aduis o98.6 °F.JMP

Answered: 54 54 56 58 58 59 60 60 60 60 60 60 60…

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

Table 14.1

54 54 56 58 58 59 60 60 60 60 60 60 60 60 61 61 61 61 61 61 61 61 62 62 62 62 62 62 62 62 62 62 62 62 62 62 62 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 65 65 65 65 65 65 65 65 66 66 66 67 67 67 67 68 68 70.

14.46) Table 14.1 provides the heights of a random sample of 93 female undergraduate students at the university of California at Irvine. Assuming that heights in this undergraduate population are normal with standar deviation o= 2.5 inches, do the data provide evidence that the mean height of all female undergraduate students at UC-Irvine is different from the mean height of 64.5 inches of all young women in the United States? Follow the four-step process as ilustatrated in Example 14.9.

this setting.
quoted value a paper in by Carl
STATE: you the for what or healthy
P-value in mind that tables can offer only P-values).
cedures, the the area or areas under
Fahrenheit or 37.0 Celsius, is widely
body you will that an oral of 98.6 degrees
printed such as B or C at back of the book to obtain the test
it the use an applet for computations or a
de not have access to technology capable of pertorming inference pro-
If yo ketch the Normal sampling distribution and the area or areas under
no J
printed keep in mind that printed tables can offer only approximate P-values).
Body temperature
EXAMPLE 14.9
ATE: When you search the internet for what constitutes "normal" or healthy
udy temperature, you will probably find that an oral temperature of 98.6 degrees
brenheit (°F), or 37.0 degrees Celsius, is considered normal. This widely
oted value comes from a paper published in 1868 by German physician Carl
Wanderlich, in which he reported more than a million body temperature read-
s In this paper, Wunderlich stated that the mean body temperature of healthy
adults is 98.6 °F. More than a century later, a study was designed to evaluate this
claim. It found a mean oral temperature of x=98.25 °F from 130 adults. Does
this study provide significant evidence that Wunderlich's claim of a mean adult
STEP
рaper,
body temperature of 98.6 °F is not correct?
PLAN: The null hypothesis is "no difference" from the accepted mean
Ou,
un = 98.6 °F. The alternative is two-sided because the study did not have a
%3D

particular in mind the data. Thus, the hypotheses
SOLVE: Check the for are the conditions"
INTRODUCTION TO INFERENCE
about the unknown mean u of the population of healthy adults are
Ho: u = 98.6
= nl
Ha: µ #98.6
SOLVE: Check the conditions for inference. Here are the "simple condition
stated on page 348.
1. SRS: The most important condition is that the 130 healthy adults in the
ple are an SRS from the population of all healthy adults. We should check thi,
requirement by asking how the data were obtained. The researchers measured
the baseline oral temperature of volunteers participating in various vaccine
clinical trials conducted at the University of Maryland. If these individuals
enrolled in the clinical trial because of a specific medical concern, for exam-
ple, the data may not be representative of the whole healthy-adult population
and could be biased. The researchers assure us that the volunteers were all
healthy. Because the subjects were volunteers, the sample is a random sample
but not a true SRS. This is very common in the life sciences, especially when
dealing with human subjects.
-wes
2. Normal distribution: We should examine the distribution of the 130 obser-
vations to look for signs that the population distribution is not Normal.
A histogram in the published report indicates that the data were roughly
Normal.
3. Known o: It is unrealistic to suppose that we know that o = 0.6 °F. This
value is based on Wunderlich's original report of a very large number of body
%3D
temperatures.
SOLVE: Obtain the test statistic and P-value. Figure 14.8 shows the output for a
one-sample z test using statistical software JMP. It gives z= -6.651 and a Pvale
rounded to zero, based on which the output specifies that we should "reject the
null hypothesis."
CONCLUDE: If u really was 98.6 °F, it would be nearly impossible to obta os
obtain an
SRS of size 130 from the healthy adult population with sample mean at fore
very strong evidence that the true mean body temperature of healthy aduis o
98.6 °F.
JMP

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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