1. This problem is a continuation of problem 2 from Homework 2. It is based on the April 2, 2022 article in The Lancet, "Reduction of dietary sodium to less than 100 mmol in heart failure (SODIUM-HF): an international, open-label, randomized, controlled trial". As in problem 2 from Homework 2, a total of 806 participants with chronic heart failure were randomly assigned to a low sodium diet (n=397) or usual care (n=409). Median age of the participants was 67 years old. Within 1 year after randomization, 22 participants in the low sodium diet group died and 17 in the usual care group died. Assume all participants were followed for a year after randomization (unless they died).
a. (*1 point) If there is no association between treatment (low sodium diet or usual care) and 1-year mortality, what would be the expected number of people who would die within 1 year if they were assigned to the low sodium diet?
b. (*1 point) What are the degrees of freedom for the chi-square test of association between treatment and 1-year mortality?
c. (*1 point) The chi-square statistic for a test of association between treatment and 1-year mortality is 0.6. The corresponding p-value is 0.45. What is the most appropriate conclusion regarding the association between treatment and 1-year mortality based on the information in the problem statement and the chi-square test? Use a significance level of 0.05. Choose the best answer:
i. There is a statistically significant association between treatment and 1-year mortality.
ii. There is not enough evidence at the 0.05 level to conclude there is an association between treatment and 1-year mortality.
iii. Treatment is not associated with 1-year mortality.
iv. Treatment is associated with a statistically significant lower risk of 1-year mortality.
v. Treatment is associated with a statistically significant higher risk of 1-year mortality.
