Problem 4. For each of the following examples, specify the null hypothesis Ho and the alternative hypothesis H1. Express your Ho and H1 using parameter(s) of the corresponding population model. If the example does not specify a population model, try coming up with one yourself. J. l l 4. A sample of size 5 is drawn at random without replacement from a population of size 2000, in which there are m males and 2000 m females and m is not known. You are interested in nding out whether there are more females than males in the population. 5. A manufacturer of household cleaning supplies advertiesd that its disinfectant product kills 99.99% of bacteria and viruses. You are interested in nding out whether the effectiveness of the advertised product is overstated. 6. A real estate developer suggests to build a private residential estate by a lake if no more than 50,000 sh live in the lake. This project is expected to be highly protable. However, an environmentalist objects strongly to the project as the living environment of the fish will be seriously damaged. You are hired by the real estate developer (or, by the environmentalist} to provide supporting evidence. 7. A group of 108 patients suffering from COVID-19 is divided into two subgroups. The first subgroup receives ordinary treatment; the second receives a candidate drug called Hydroxychloroquine. The study will record whether each patient's condition improves, worsens or stays unchanged over a period of two weeks. You, a reseacher at FDA! CDC, want to decide whether to recommend Hydroxychloroquine as an effective drug for COVID19. Problem 5. For numbers 47 of the previous problem: 1. Describe the random variables that you would like to obtain in a sample [for example, '11 iid draws from a N{p,oz) distribution'). 2. Dene a test statistic that would allow you to test your hypothesis- 3. Derive the asymptotic distribution of your statistic under the null hypothesis. 4. Derive the critical value for your test at a given a signicance level. 5. Derive the p-value of your test