You may have heard that Botox (botulinum toxin type A) is used for cosmetic surgery, but could it have other beneficial uses? A total of 31 patients who suffered chronic low-back pain were randomly assigned to receive 200 units of either Botox or saline solution through 5 injections at 5 different locations in their backs. The saline injection was not expected to reduce pain but was given as a placebo treatment. Pain relief was defined as a patient’s pain level being reduced to less than half of the original pain level after 8 weeks. Here are the results:

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

b. Explain why you should not use the methods of this section to calculate the P-value.

c. We performed 100 trials of a simulation to see what differences in proportions would occur due only to chance variation in the random assignment, assuming that the type of injection (Botox or saline) doesn’t matter. A dotplot of the results is shown here. What is the estimated P-value?

d. What conclusion would you draw?

Transcribed Image Text:

Botox Saline Total Pain relief 10 3 13 No pain relief 5 13 18 Total 15 16 31