Question

A random sample of 15 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: 9, 12, 8, 12, 7, 5, 5, 6, 6, 11, 12, 11, 10, 8, 10 Send data to Excel Under the assumption that co-payment amounts are normally distributed, find a 90% confidence interval for the mean co-payment amount in dollars. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.) What is the lower limit of the confidence interval? What is the upper limit of the confidence interval?

Answer 1

From the given data: = 8.8 and s = 2.569

Since population standard deviation is unknown and n < 30, we use the t distribution

the t critical at = 0.10, df = n - 1 = 14 is 1.76

The Confidence interval is given by ME

ME = t critical * s / sqrt(n) = 1.76 * 2.569 / sqrt(15) = 1.167

The Lower Limit = 8.8 - 1.167 = 7.633       7.6

The Upper Limit = 8.8 + 1.167 = 9.967    10.0