Assignment 1: Confidence Interval for one sample continuous outcome, sample size >=30.? 1. Suppose you are a junior researcher of a research team. You want

Assignment 1: Confidence Interval for one sample continuous outcome, sample size >=30. 

1. Suppose you are a junior researcher of a research team. You want to know the true mean age of 2,500 freshmen students of MSU. You have randomly selected 144 freshmen (n=144), and collected their age. The mean age x¯ = 25.3 years with a standard deviation s = 5.7.

a. Compute a 95% confidence interval (CI) for the true mean age of freshmen. (10 points).

b. Interpret your findings. (5 points).

Assignment 2: Confidence Interval for one sample continuous outcome, sample size <30. 

Now assume that due to time and money constraints, you have collected data (age) only from 28 students (n=28) with the mean x¯ =24.2 years and standard deviation s = 4.3.

a. Compute a 95% confidence interval (CI) for the true mean age for freshmen (10 points).

b. Interpret your findings (5 points).

c. Is there any difference between when you have collected data from 144 students and you have collected data from only 28 students? If so, what are the difference? Why it happens? (5 bonus points). 

Assignment 3: Confidence Interval for one sample dichotomous outcome 

In a sample of 1,540 patients attending at emergency room (ER) department, 231 patients were diagnosed with cardiac failure.

a. Calculate the confidence interval for patients with heart failure with 90% confidence level. (10 points).

b. Interpret the findings. (5 points)