The table below contains data from a study in which patients with HIV were randomly assigned to two groups; one group getting cannabis as pain relief and the other getting a placebo. All the patients had severe pain and the response variable was whether or not pain was reduced significantly. One question the researchers had was “Is cannabis more effective than a placebo in relieving pain in HIV patients?”

	Cannabis	Placebo
Pain reduced significantly	27	28
Pain not reduced significantly	29	53
Total	56	81

When answering the questions below, make sure you use appropriate notation where necessary.

What are the null and alternative hypotheses for the research question in bold above?

Calculate the sample proportions of patients with reduced pain in each group. What is the sample statistic for this hypothesis test?

Using one or two sentences, explain the main assumption we make when conducting a hypothesis test using a randomisation distribution.

Generate a randomisation distribution of 10,000 differences in proportions. This can be created in StatKey using the ‘Randomisation Hypotheses Tests – Test for Difference in Proportions’ tool or another technology. Include this plot with an appropriate title and axis labels in your assignment.

Describe the shape and centre of your randomisation distribution in one or two sentences.

Use your randomisation distribution to estimate a p-value for the test. Explain in one or two sentences or with a diagram/image how you found the p-value.

If the researchers are using a significance level of α = 0.05, what would their decision and conclusion for this hypothesis test be?

If the researchers used a significance level of α = 0.10, would their decision and conclusion have been different? Explain your answer in one or two sentences.