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StatisticsQ&A LibraryAnkylosing spondylitis is an inflammatory disease which affects the spine and sacroiliac joint and can lead to the fusing of vertebrae in the spine. Exercise is important in helping manage pain, therefore a pharmaceutical company wanted to test if their new biologic would increase the time a patient could exercise before experiencing discomfort. The following table gives the time (in minutes) seven patients were able to exercise before reporting pain, both at baseline and then again after six months of taking the biologic.Exercise Time (in minutes)Subject 1 Baseline 30 Post-treatment 40Subject 245 40Subject 350 60Subject 435 37Subject 555 60Subject 620 25Subject 775 75Assume the population(s) of all exercise times is (are) normally distributed. Use JMP to test whether the evidence suggests that the time a person with ankylosing spondylitis can exercise before experiencing discomfort increases after taking this new biologic. Validate the test statistic from JMP by computing it manually. Complete the multi-step hypothesis testing process we learned in class to arrive at a conclusion.Question

Asked Nov 24, 2019

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Ankylosing spondylitis is an inflammatory disease which affects the spine and sacroiliac joint and can lead to the fusing of vertebrae in the spine. Exercise is important in helping manage pain, therefore a pharmaceutical company wanted to test if their new biologic would increase the time a patient could exercise before experiencing discomfort. The following table gives the time (in minutes) seven patients were able to exercise before reporting pain, both at baseline and then again after six months of taking the biologic.

Exercise Time (in minutes)

Subject 1 Baseline 30 Post-treatment 40

Subject 2

45 40

Subject 3

50 60

Subject 4

35 37

Subject 5

55 60

Subject 6

20 25

Subject 7

75 75

Assume the population(s) of all exercise times is (are) normally distributed. Use JMP to test whether the evidence suggests that the time a person with ankylosing spondylitis can exercise before experiencing discomfort increases after taking this new biologic. Validate the test statistic from JMP by computing it manually. Complete the multi-step hypothesis testing process we learned in class to arrive at a conclusion.

Step 1

Denote *μ _{1}* as the true mean of baseline and

The hypotheses appropriate for the test are as follows:

*Null hypothesis:*

*H*_{0}: *μ _{1 }*=

*Alternate hypothesis:*

*H*_{1}:* μ _{1 }*<

Let *μ _{d}* denote the difference between means of baseline and post-treatment. That is,

*μ _{d }*=

In this case, the appropriate test is paired t test,

The test statistic is *t *which is calculated as,

Step 2

where *d*-bar is the mean of the differences, µ_{d0} is the hypothesized mean difference, *s _{d}*-bar is the standard deviation of the differences.

*Degrees of freedom:*

For student’s* t *distribution, the degrees of freedom is *n* –1.

The number of observations is 7.

Thus, the test statistic is distributed as Student’s *t* with 6 degrees of freedom.

The differences for the two samples are –10, 5,–10, –2, –5, –5, and 0.

The mean and standard deviation are obtained as follows:

Step 3

The test statistic is obt...

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