Answered: The authors of a paper randomly…

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

The authors of a paper randomly selected two samples of patients admitted to the hospital after suffering a stroke. One sample was selected from patients who received biofeedback weight training for 8 weeks, and the other sample was selected from patients who did not receive this training. At the end of 8 weeks, the time it took (in seconds) to stand from a sitting position and then to sit down again (called sit-stand-sit time) was measured for the people in each sample. Data consistent with summary quantities given in the paper are given below. For purposes of this exercise, you can assume that the samples are representative of the population of stroke patients who receive the biofeedback training and the population of stroke patients who do not receive this training.

Biofeedback Group

2.2

2.9

4.6

2.4

3.0

4.4

3.5

4.3

3.5

3.8

3.1

3.8

2.6

3.4

No Biofeedback Group

5.2

4.8

4.0

4.3

4.8

4.4

4.3

5.2

3.5

4.3

5.2

4.5

4.1

3.5

4.0

Conduct a test of hypothesis to test whether the mean sit-stand-sit time for group that received the biofeedback training was shorter than for the group without the training.

Find the test statistic. (Round your answer to one decimal place.)

t =

Find the df. (Round your answer down to the nearest whole number.)

df =

Find the P-value. (Round your answer to three decimal places.)

P-value =

State your conclusion.

Fail to reject H₀. We have convincing evidence that the mean sit-stand-sit time for the biofeedback group is shorter than the mean sit-stand-sit time for the no training group.Reject H₀. We do not have convincing evidence that the mean sit-stand-sit time for the biofeedback group is shorter than the mean sit-stand-sit time for the no training group. Reject H₀. We have convincing evidence that the mean mean sit-stand-sit time for the biofeedback group is shorter than the mean sit-stand-sit time for the no training group.Fail to reject H₀. We do not have convincing evidence that the mean sit-stand-sit time for the biofeedback group is shorter than the mean sit-stand-sit time for the no training group.

Use the given data to construct a 95% confidence interval for the difference in mean sit-stand-sit time for these two populations. (Use ?_biofeedback − ?_{no biofeedback}. Round your answers to three decimal places.)

to seconds

Interpret the interval.

We are 95% confident that, for patients in the sample, the difference between the mean sit-stand-sit time for patients who received the biofeedback training and the patients who did not receive biofeedback training is between these two values.There is a 95% chance that the true difference between the mean sit-stand-sit time for patients who received biofeedback training and the patients who did not receive biofeedback training is directly in the middle of these two values. There is a 95% chance that, for patients in the sample, the difference between the mean sit-stand-sit time for patients who received the biofeedback training and the patients who did not receive biofeedback training is between these two values.There is a 95% chance that the true difference between the mean sit-stand-sit time for patients who received the biofeedback training and the patients who did not receive biofeedback training is between these two values.We are 95% confident that the true difference between the mean sit-stand-sit time for patients who received the biofeedback training and the patients who did not receive biofeedback training is between these two values.

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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