Confidence interval help please! Upper and lower limits?

Question

A random sample of 9 health maintenance organizations (HMOs) was selected. For each HMO, the co-payment (in dollars) for a doctor's office visit was recorded. The results are as follows:

12, 12, 6, 10, 10, 9, 9, 10, 6

Under the assumption that co-payment amounts are normally distributed, find a 95% confidence interval for the mean co-payment amount in dollars.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.

What is the lower limit of the confidence interval?

What is the upper limit of the confidence interval?

Please help me out, thanks!

Answer 1

The standard deviation for this data set is 2.179. It sounds like they want you to calculate it manually from the mean and the deviations. You do this as follows:

   1. Find the mean, m, of the values.

   2. For each value x(i) calculate its deviation (x(i) -m ) from the mean.

   3. Calculate the squares of these deviations.

   4. Find the mean of the squared deviations. This quantity is the variance σ^2.

   5. Take the square root of the variance and you have the standard deviation, σ

The 95% confidence interval is the range covered by ± 1.92σ from the mean 9.333.

5.062 to 13.604 is the range from lower to upper 95% confidence limits