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 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.

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.

Accepted Answer

Consider the given data: