Question 3 Albumin is a protein produced by the liver. Since Hepatitis C causes liver damage, one might suspect that people with hepatitis C would have lower albumin levels than healthy people. Although this is quite reasonable, it still requires evidence from data. We can classify the progress of Hepatitis C in three: (1) Hepatitis; (2) Fibrosis; and (3) Cirrhosis. A random sample of 74 patients with Hepatitis C was drawn. The table below shows the summary of the data: Table 1: Summary statistics of albumin levels in patients with Hepatitis C category Sample Mean Sample Std. Dev Hepatitis 13.83 3.51 24 Fibrosis 41.76 3.74 21 Cirrhosis 32.48 5.82 The medical community has established that the average albumin level in people with a healthy liver is 14g/L with a standard deviation of 5g/L. a. The summary table shows that patients with Fibrosis presented an average albumin level of 41.76g/L. If the liver of patients with Hepatitis C at the stage of Fibrosis had the same liver functionality as Healthy patients, regarding to albumin levels, what would be the probability of observing an average albumin level at least as low as the one we observed? List what assumptions you are making, if any. 1 marks b. What is the probability that a healthy patient has an albumnin level lower than the sample average of patients with Fibrosis, i.e., 41.767 [1 marks] c. Calculate a confidence interval of 97%% for the mean albumin level of patients with Fibrosis. Does the interval contain the value 44g/L? List what assumptions you are making, if any. [3 marks] d. At a 3% significance level, do we have enough evidence to state that patients with Fibrosis have a lower average albumin level than healthy patients? (4 marks] 1. State the null and alternative hypotheses in the context of the question in words. 2. Compute the test statistic 3. Calculate the p-value. 4. What is your conclusion? e. Calculate the 97% confidence interval for the average albumin level of patients for the Hepatitis group. Does this interval contain 44g/L? [2 marks) f. Test the same hypotheses you tested in item (d), at a 3%% significance level, but this time using the Hepatitis group. Again, make sure to compute the test statistic, p-value and state your conclusion. [2 marks]