# In a 2001 study, researchers investigated the effects of Botox on chronic low back pain.

In a 2001 study, researchers investigated the effects of Botox on chronic low back pain. They studied 31 patients who suffered from severe chronic low back pain, randomly assigning 15 of those patients to receive the drug botulinum (Botox) and the remaining 16 to receive a normal saline injection. At the end of eight weeks, 10 of the 15 subjects in the Botox group had experienced substantial relief, compared to 4 of 16 in the group that had received a normal saline injection.

a.    Identify the explanatory and response variables in this study.

Classify them as categorical (binary?) or quantitative.

Explanatory variable:                                    Type:

Response variable:                                         Type:

b. Was this an observational study or an experiment? Explain carefully how you know.

c. Organize the given data in a two-way table. [Hint: put the explanatory variable groups in columns.]

d. For EACH treatment group, calculate the conditional proportions for patients who experienced substantial relief.

e. Use Minitab to construct a segmented bar graph comparing the proportions of those who experienced substantial relief in the two groups. Make sure to label your axes carefully. Include a printout of your graph in your submission.

f. Comment on what your graph in part (e) reveals. Also, does this study provide some reasonable evidence to conclude that using Botox causes a reduction in back pain? Explain your answer, supporting what you write with numbers.

g. Calculate manually and interpret a 90% confidence interval for the proportion of Botox-takers who experience substantial pain relief. Show all of your work. [Hint: Your interpretation should say “I am 90% confident that for someone who receives Botox, …”]

h. Calculate manually and interpret a 90% confidence interval for the proportion of saline-takers who experience substantial pain relief. Show all of your work.

i. Based on your above confidence intervals, does it seem as if the study provides strong evidence that Botox led to a higher chance of pain relief? Explain your answer.

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