For a particular illness, there are two possible treatments: Medicine A and Medicine B. It is known that there is an unwanted, but non-life-threatening, side effect of both of these medicines. A hospital is conducting a study to determine if these medicines are equally likely to cause this side effect to help them determine which medicine they should use. Over a period of 3 months the hospital randomly allocates one of these medicines to patients with this particular illness. During the study period 250 patients were given Medicine A, and 135 of these patients had the side effect. During the study period 240 patients were given Medicine B, and 96 of these patients had the side effect. You will perform a hypothesis test to determine if there is a difference between the two medicines in terms of the probability that a person taking that medicine will have the side effect. In the following parts all calculations must be done by hand, unless otherwise specified. (a) (1 point) What kind of hypothesis test will you be doing? (b) (4 points) Define the variables and parameter of interest. (c) (2 points) What are the null and alternative hypotheses? (d) (3 points) Calculate the estimate for the parameter of interest. (e) (3 points) Calculate the appropriate test statistic. (f) (2 points) Calculate the p-value (you will need to use Matlab). (g) (2 points) Based on the p-value do you reject or retain the null hypothesis at the 5% level of significance? Provide justification for your answer. (h) (1 point) Summarise your conclusion from Part (g) in the context of the question. (i) (4 points) Calculate the 95% confidence interval for the parameter of interest. (j) (1 point) Summarise your confidence interval in the context of the question.