Question 4. 1) Let X be a drug against COVID-19. The effectiveness of the drug is equal to the sum of the first 7 numbers in your dataset out of 100 total applications. For example, the sum of the...

Extracted text: Question 4. 1) Let X be a drug against COVID-19. The effectiveness of the drug is equal to the sum of the first 7 numbers in your dataset out of 100 total applications. For example, the sum of the first 7 numbers in my dataset is equal to 30, it means that the drug X has been effective in 30 out of 100 cases. I would like to test the hypothesis that the effectiveness of the drug X is equal to 90%. Obtain the asymptotic distribution of drug effectiveness p and test the two tailed hypothesis at a = 5%; 2) Now suppose we have 2 drugs X and Y against COVID-19. The effectiveness of X in 100 cases has been found to be equal to the sum of the first 10 numbers in your dataset, while the effectiveness of Y in 100 cases has been found to be equal to the first 8 numbers in your dataset. Write down the approximate distribution of the difference between sample means. Test the hypothesis that both drugs have the same effectiveness at a = 5%; 3) Now suppose that there are three drugs available against COVID-19, X,Y and Z. People have strict preference for a particular type of drug. We sampled 100 people and we can group them into three categories based on their preferences: Group A strictly prefers X over Y and Z and the number of such people in the sample is equal to the sum of the first 5 numbers in your dataset. Group B strictly prefers Y over the other 2 available drugs and the number of such people in our sample is equal to the sum of the first 7 numbers in your dataset. And Group C strictly prefers Z over the other 2, and the number of such people in our sample is equal to (100 – number of people in Group A – number of people in group B). Test the hypothesis that the proportions of people preferring each drug is the same at a = 5%


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