In 1980, the active ingredient in marijuana was shown to outperform a placebo in reducing nausea in chemotherapy patients, with a p-value of 0.0004. Many studies are now underway to see if the drug has additional medicinal uses. In one controlled, randomized trial, 55 patients with HIV were randomly assigned to two groups, with one group getting cannabis (marijuana) and the other getting a placebo. All of the patients had severe neuropathic pain, and the response variable is whether or not pain was reduced by 30% or more (a standard benchmark in pain measurement). The results are shown in Table 4.15. The question of interest is whether marijuana is more effective than a placebo in relieving pain.

Table 4.15

(a) What are the null and alternative hypotheses?

(b) What are the sample proportions of patients with reduced pain in each group? Are the sample results in the direction of the alternative hypothesis?

(c) The US Food and Drug Administration (FDA) is reluctant to approve the medicinal use of cannabis unless the evidence supporting it is very strong because the drug has significant side effects. Do you expect the FDA to use a relatively small or relatively large significance level in making a conclusion from this test?

(d) What assumption do we make in creating the randomization distribution? If we use the difference in sample proportions, D = pÌ‚₁ ˆ’ pÌ‚₂, as our sample statistic, where will the distribution be centered? Give a rough sketch of the general shape of the randomization distribution, showing the shape and where it is centered

(e) What is the observed statistic from the sample? If the p-value for this test is 0.02, locate the observed statistic on your rough sketch of the randomization distribution.

(f) Use the p-value given in part (e) to give an informal conclusion to the test by describing the strength of evidence for the result. 

(g) Combining your answers to parts (c) and (f), what is the likely formal conclusion of the test?

Transcribed Image Text:

Pain Not Reduced Pain Reduced Cannabis 14 13 21 Placebo