Question

In a simple random sample of 120 Kansas seniors you found the mean out-of-pocket health care expenses for 2008 to be $4, 897. Assume σ=2,125.
i) How many people would you have to sample to estimate the mean out-of-pocket health care expenses in 2008 for all Kansas seniors to within $200 with 99% confidence?

ii) Calculate and interpret a 98% confidence interval for the mean out-of-pocket health care expenses in 2008 for all Kansas seniors.
iii) What is the margin of error for the interval calculated in part ii?

Answer 1

i) The margin of error is given by

Here for 99% confidence the critical value

Using and moe=200 we have

ii) The confidence interval is given by

   For 98% confidence interval

So the interval is

Thus the interval is

There is 98% chance that mean out-of-pocket health care expenses in 2008 for all Kansas seniors lies in between 4445.79 to 5349.21

iii) The margin of error is