The following is data about the hemoglobin concentrations of volunteers collected at sea level and at an altitude of 11000 feet. sea level concentrations = [14.70 , 15.22, 15.28, 16.58, 15.10 , 15.66, 15.91, 14.41, 14.73, 15.09, 15.62, 14.92] 11000 feet concentrations = [14.81, 15.68, 15.57, 16.59, 15.21, 15.69, 16.16, 14.68, 15.09, 15.30 , 16.15, 14.76] There are two alternative scenarios about the way the data were obtained. In scenario 1, there are 12 volunteers who lived for a month at sea level, at which time blood was drawn and the data in "sea level concentrations" dataset were obtained. Subsequently, all 12 volunteers were moved to 11000 ft and after a month the data in the "11000 feet concentrations" dataset obtained. There is a one to one correspondence between the numbers in the two datasets, that is the first numbers correspond to volunteer1, the second numbers to volunteer2 etc. In scenario 2, the "sea level concentrations" dataset is a random sample obtained from 12 people living at sea level and the "11000 feet concentrations" dataset is a random sample obtained from 12 different people living at 11000 feet. In this case there is no correlation between the individual numbers in the two datasets. For each of these scenarios, calculate the standard errors of the mean differences or difference between of the means of the samples as well as the corresponding 95% confidence intervals. Perform the appropriate t-test for each scenario. Assume equal variances between the samples and two-tailed hypotheses. Round off all answers to two digits after the decimal point. Since the sign of the t-statistic depends on the arbitrary choice of which data to subtract from which and to simplify grading, wherever applicable report the absolute value of the t-statistic. In scenario 1, what is the absolute value of the t-statistic required to carry out an appropriate t-test to check if altitude has an effect on hemoglobin concentrations? In scenario 1, what is the p-value obtained from an appropriate t-test to check if altitude has an effect on hemoglobin concentrations? 0.001-0.01 0.01-0.02 0.02-0.05 0.05-0.10 greater than 0.10

The following is data about the hemoglobin concentrations of volunteers collected at sea level and at an altitude of 11000 feet. sea level concentrations = [14.70 , 15.22, 15.28, 16.58, 15.10 , 15.66, 15.91, 14.41, 14.73, 15.09, 15.62, 14.92] 11000 feet concentrations = [14.81, 15.68, 15.57, 16.59, 15.21, 15.69, 16.16, 14.68, 15.09, 15.30 , 16.15, 14.76] There are two alternative scenarios about the way the data were obtained. In scenario 1, there are 12 volunteers who lived for a month at sea level, at which time blood was drawn and the data in "sea level concentrations" dataset were obtained. Subsequently, all 12 volunteers were moved to 11000 ft and after a month the data in the "11000 feet concentrations" dataset obtained. There is a one to one correspondence between the numbers in the two datasets, that is the first numbers correspond to volunteer1, the second numbers to volunteer2 etc. In scenario 2, the "sea level concentrations" dataset is a random sample obtained from 12 people living at sea level and the "11000 feet concentrations" dataset is a random sample obtained from 12 different people living at 11000 feet. In this case there is no correlation between the individual numbers in the two datasets. For each of these scenarios, calculate the standard errors of the mean differences or difference between of the means of the samples as well as the corresponding 95% confidence intervals. Perform the appropriate t-test for each scenario. Assume equal variances between the samples and two-tailed hypotheses. Round off all answers to two digits after the decimal point. Since the sign of the t-statistic depends on the arbitrary choice of which data to subtract from which and to simplify grading, wherever applicable report the absolute value of the t-statistic. In scenario 1, what is the absolute value of the t-statistic required to carry out an appropriate t-test to check if altitude has an effect on hemoglobin concentrations? In scenario 1, what is the p-value obtained from an appropriate t-test to check if altitude has an effect on hemoglobin concentrations? 0.001-0.01 0.01-0.02 0.02-0.05 0.05-0.10 greater than 0.10

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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The following is data about the hemoglobin concentrations of volunteers collected at sea level and at an altitude of 11000 feet.

sea level concentrations =
[14.70 , 15.22, 15.28, 16.58, 15.10 , 15.66, 15.91, 14.41, 14.73, 15.09, 15.62, 14.92]

11000 feet concentrations = [14.81, 15.68, 15.57, 16.59, 15.21, 15.69, 16.16, 14.68, 15.09, 15.30 , 16.15, 14.76]

There are two alternative scenarios about the way the data were obtained.

In scenario 1, there are 12 volunteers who lived for a month at sea level, at which time blood was drawn and the data in "sea level concentrations" dataset were obtained. Subsequently, all 12 volunteers were moved to 11000 ft and after a month the data in the "11000 feet concentrations" dataset obtained. There is a one to one correspondence between the numbers in the two datasets, that is the first numbers correspond to volunteer1, the second numbers to volunteer2 etc.

In scenario 2, the "sea level concentrations" dataset is a random sample obtained from 12 people living at sea level and the
"11000 feet concentrations" dataset is a random sample obtained from 12 different people living at 11000 feet. In this case there is no correlation between the individual numbers in the two datasets.

For each of these scenarios, calculate the standard errors of the mean differences or difference between of the means of the samples as well as the corresponding 95% confidence intervals. Perform the appropriate t-test for each scenario. Assume equal variances between the samples and two-tailed hypotheses.

Round off all answers to two digits after the decimal point. Since the sign of the t-statistic depends on the arbitrary choice of which data to subtract from which and to simplify grading, wherever applicable report the absolute value of the t-statistic.

In scenario 1, what is the absolute value of the t-statistic required to carry out an appropriate t-test to check if altitude has an effect on hemoglobin concentrations?

In scenario 1, what is the p-value obtained from an appropriate t-test to check if altitude has an effect on hemoglobin concentrations?

		0.001-0.01
		0.01-0.02
		0.02-0.05
		0.05-0.10
		greater than 0.10

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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