Table 6.11 shows data on whether or not a treatment relieved pain for patients. Test whether the treatment is significantly better than a placebo at relieving pain. The patients were randomly allocated to the two groups and the experiment was double-blind.

Table 6.11

(a) Find the relevant sample proportions in each group and the pooled proportion.
(b) Complete the hypothesis test using the normal distribution and show all details.

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Placebo Total Treatment 36 Relieved pain Did not relieve pain 57 93 21 39 54 75 150 Total 75