Problem 1. I 1 + 1+ 1 + 2 =5 marks] Nearly 75% of all death in the United States are attributed to just 10 causes, with the top four of these accounting for over 50% of all non accidental deaths as follows: heart disease (23.4%), cancer (22.5%), respiratory disease (5.6%), and stroke (5.1%). The study of the causes of n =308 non accidental dea :hs at a local hospital gave the following counts. Cause Heart Cancer Respiratory Stroke Other Disease Disease Deaths 78 81 28 16 105 308 Do the data provide sufficient information to indicate that the proportions of deaths at this hospital differ significantly from the proportions in the population in the country? Test appropriate hypothesis at 5% level of significance using R. For full solution give the answers to questions 1, 2, 3, and 4. 1. [1 mark} State the null and alternative hypotheses you are going to test. 2. [1 mark} Represent frequency table with categories Heart Disease Cancer Respiratory Disease Stroke Other Show the code, required to answer questions 2, in blue or red, and corresponding R output in black. 3. [1 mark} Perform chi - square test and represent its results. Show the code, required to answer questions 3, in blue or red, and corresponding R output in black. 4. [2 marks) Make the conclusions about truth or falsity of stated hypotheses. Decide whether the proportions of deaths at the hospital differ significantly from the proportions of deaths in USA population