Comprehensive Task ("Cholesterol Problem") According Mayo clinic website, "cholesterol is a waxy substance found in your blood. Your body needs cholesterol to build healthy cells, but high levels of cholesterol can increase your risk of heart disease. With high cholesterol, you can develop fatty deposits in your blood vessels. Eventually, these deposits grow, making it difficult for enough blood to flow through your arteries. Sometimes, those deposits can break suddenly and form a clot that causes a heart attack or stroke." Moreover, according to the Center for Disease Control (CDC), the normal cholesterol level for US adults is 199 mg/dL. However, there is a concern that average cholesterol level in all heart-attack patients may actually be more than the normal cholesterol level for US adults, and we have been asked to investigate. Here are the cholesterol levels (measured in mg/dL) for 30 heart-attack patients, and as well as the its summary statistics, and dot plot . 142 221 236 276 288 160 224 242 278 288 186 226 244 280 294 206 229 266 280 310 210 234 270 282 318 220 236 272 282 360 Summary Statistics: n=30 mean = 252 St. Dev =46.63 Q1=224.5 med=255 Q3=281. 1. In the space below, draw a boxplot for this dataset. 2. In order for us to use this sample of 30 heart-attack patients to make inferences about the whole population of heart-attack patients, what assumption must we make regarding the sample and how it was obtained? What risk do we run in performing any inference about the population of interest if this assumption is not met?3. Assuming that the sampling was done properly, name two ways in which the summary information and graphs above suggest that the population average cholesterol level might be more than 199 mg/dL? 4. Based on our analysis of our sample data, we are asked to perform a formal hypothesis test (test of significance) to examine if the average cholesterol level of all heart-attack patients may actually be more than 199 mg/dL. 5. Develop the correct null and alternative hypotheses using standard statistics symbols, using words, or using both. 6. Based on the context of the question we are investigating and the nature of our sample data: a. Choose an appropriate test procedure and list that procedure here. b. State any assumptions or conditions regarding your sample and/or the population that are necessary for the test procedure you have chosen. c. Compute the correct test statistic value and record that value here to 3 decimal places. d. Compute the correct p-value based on both your hypotheses(in Question # 5 ) and the test statistic(in Question# 6c) and record that p-value here to 7 decimal places. e. Using a significance level of 5%, state clearly if you are rejecting the null hypothesis or failing to reject the null hypothesis. (Circle only one.) Reject the null hypothesis Fail to reject the null hypothesis Printed 10/18/22 Page 68. A journalist is writing an article about the results of your investigation and has asked you for a one or two sentence quote to include in the article. The journalist asks "What was the purpose of the investigation? What did you conclude? Keep in mind that our readers probably never took a statistics course." In the space below, write one or two sentences that answer both of the journalist's questions in a way that is easily understood by the general public AND is consistent with your work in Question # 6e