Elissa Epel, a professor of health psychology at the University of California–San Francisco, studied women in high- and low-stress situations. She found that women with higher cortisol responses to stress ate significantly more sweet food and consumed more calories on the stress day compared with those with low cortisol responses, and compared with themselves on lower stress days. Increases in negative mood in response to the stressors were also significantly related to greater food consumption. These results suggest that psychophysiological responses to stress may influence subsequent eating behavior. Over time, these alterations could impact both weight and health. You are interested in studying whether students living in the dorms or students living off campus have higher cortisol levels. You ask a sample of n₁ = 25 students living in the dorms and n₂ = 30 students living off campus to record their afternoon cortisol levels for a week. The average cortisol level for students living in the dorms was M₁ = 0.259 μg/dl, with a standard deviation of s₁ = 0.131. The average cortisol level for students living off campus was M₂ = 0.237 μg/dl, with a standard deviation of s₂ = 0.128. To develop a confidence interval for the population mean difference μ₁ – μ₂, you need to calculate the estimated standard error of the difference of sample means, s(M1 – M2)(M1 – M2). The estimated standard error is s(M1 – M2)(M1 – M2) = . Use the Distributions tool to develop a 99% confidence interval for the difference in the mean cortisol level of students living in the dorms and students living off campus. 0123 Standard Normalt Distribution Select a Distribution The 99% confidence interval is to . This means that you are % confident that the unknown difference between the mean cortisol level of the population of students living in the dorms and the population of students living off campus is located within this interval. Use the tool to construct a 90% confidence interval for the population mean difference. The 90% confidence interval is to . This means that you are % confident that the unknown difference between the mean cortisol level of the population of students living in the dorms and the population of students living off campus is located within this interval. The new confidence interval is than the original one, because the new level of confidence is than the original one.

Elissa Epel, a professor of health psychology at the University of California–San Francisco, studied women in high- and low-stress situations. She found that women with higher cortisol responses to stress ate significantly more sweet food and consumed more calories on the stress day compared with those with low cortisol responses, and compared with themselves on lower stress days. Increases in negative mood in response to the stressors were also significantly related to greater food consumption. These results suggest that psychophysiological responses to stress may influence subsequent eating behavior. Over time, these alterations could impact both weight and health. You are interested in studying whether students living in the dorms or students living off campus have higher cortisol levels. You ask a sample of n₁ = 25 students living in the dorms and n₂ = 30 students living off campus to record their afternoon cortisol levels for a week. The average cortisol level for students living in the dorms was M₁ = 0.259 μg/dl, with a standard deviation of s₁ = 0.131. The average cortisol level for students living off campus was M₂ = 0.237 μg/dl, with a standard deviation of s₂ = 0.128. To develop a confidence interval for the population mean difference μ₁ – μ₂, you need to calculate the estimated standard error of the difference of sample means, s(M1 – M2)(M1 – M2). The estimated standard error is s(M1 – M2)(M1 – M2) = . Use the Distributions tool to develop a 99% confidence interval for the difference in the mean cortisol level of students living in the dorms and students living off campus. 0123 Standard Normalt Distribution Select a Distribution The 99% confidence interval is to . This means that you are % confident that the unknown difference between the mean cortisol level of the population of students living in the dorms and the population of students living off campus is located within this interval. Use the tool to construct a 90% confidence interval for the population mean difference. The 90% confidence interval is to . This means that you are % confident that the unknown difference between the mean cortisol level of the population of students living in the dorms and the population of students living off campus is located within this interval. The new confidence interval is than the original one, because the new level of confidence is than the original one.

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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You are interested in studying whether students living in the dorms or students living off campus have higher cortisol levels. You ask a sample of n₁ = 25 students living in the dorms and n₂ = 30 students living off campus to record their afternoon cortisol levels for a week.

The average cortisol level for students living in the dorms was M₁ = 0.259 μg/dl, with a standard deviation of s₁ = 0.131. The average cortisol level for students living off campus was M₂ = 0.237 μg/dl, with a standard deviation of s₂ = 0.128.

To develop a confidence interval for the population mean difference μ₁ – μ₂, you need to calculate the estimated standard error of the difference of sample means, s(M1 – M2)(M1 – M2). The estimated standard error is s(M1 – M2)(M1 – M2) = .

Use the Distributions tool to develop a 99% confidence interval for the difference in the mean cortisol level of students living in the dorms and students living off campus.

0123

Standard Normalt Distribution

Select a Distribution

The 99% confidence interval is to .

This means that you are % confident that the unknown difference between the mean cortisol level of the population of students living in the dorms and the population of students living off campus is located within this interval.

Use the tool to construct a 90% confidence interval for the population mean difference. The 90% confidence interval is to .

The new confidence interval is than the original one, because the new level of confidence is than the original one.

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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Step 1

Provided data is:

n₁=25	n₂=30
M₁=0.259	M₂=0.237
s₁=0.131	s₂=0.128

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