Please explain all work.
In order for a lifestyle change to be considered effective, the target is to have the average cholesterol of this group be below 200. After 6 months of exercising more and eating better, an SRS of 51 patients at risk for heart disease had an average cholesterol of x = 192, with a standard deviation s = 21. Is this sufficient evidence that eating better and exercising more is effective in meeting the target? Assume the distribution of the cholesterol for patients in this group is approximately Normal with mean μ.
a) State the null and Alternative hypotheses H0:
b) What are the degrees of freedom?
c) Find the one-sample t-statistic
d) Use the t-table to estimate the P-value and state your conclusion in words of this problem
e) Find a 95% confidence interval for the average cholesterol of patients at risk for heart disease who have been on the diet for 6 months
A Complete, Neat and Step-by-step Solution is provided in the attached file.