A pharmaceutical company wants to test whether the incidence of side effects (i.e. adverse events)differs between the treatment and placebo groups at theα= 0.05. Letp1= the proportion of subjects in the treatment groups who experienced at least one adverse event and letp2= the proportion of subjects in the placebo group who experience at least one adverse event. 8 out of 30 people in the treatment group experienced at least one adverse event and 5 out of 30 people in the placebo group experienced at least one adverse event. (a) Set up the null and alternative hypothesis (using mathematical notation/numbers AND interpret them in the context of the problem) (b) Calculate the test statistic (c) Calculate the critical value (d) Draw a picture of the distribution of the test statistic under H0. Label and provide values for the critical value and the test statistic, and shade the critical region. (e) Make and justify a statistical decision at theα= 0.05 level and state your conclusions in the context of the problem. (f) If we increased the sample size to be very large but kept the sample proportion the same how would you expect your decision of this hypothesis test to change?
4. A pharmaceutical company wants to test whether the incidence of side effects (i.e. adverse events)differs between the treatment and placebo groups at theα= 0.05. Letp1= the proportion of subjects in the treatment groups who experienced at least one adverse
(a) Set up the null and alternative hypothesis (using mathematical notation/numbers AND interpret them in the context of the problem)
(b) Calculate the test statistic
(c) Calculate the critical value
(d) Draw a picture of the distribution of the test statistic under H0. Label and provide values for the critical value and the test statistic, and shade the critical region.
(e) Make and justify a statistical decision at theα= 0.05 level and state your conclusions in the context of the problem.
(f) If we increased the
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