Question

A healthcare provider monitors the number of CAT scans performed each month in each of its clinics. The most recent year of data for a particular clinic follows (the reported variable is the number of CAT scans each month expressed as the number of CAT scans per thousand members of the health plan): 2.31 2.09 2.36 1.95 1.98 2.25 2.16 2.07 1.88 1.94 1.97 2.02 (a) Find a 95% two-sided confidence interval on the mean number of CAT scans performed each month at this clinic. (b) Historically, the mean number of scans performed by all clinics in the system has been 1.95. Is there any evidence that this particular clinic performs more CAT scans on overage than the overall system average?

Answer 1

a) 95% two-sided confidence interval on the mean number of CAT scans is

between 1.98 and 2.18

b) Yes. In 95% confidence, the particular clinic outperform than the overall system average.

Explanation:

(a)

Confidence interval can be calculated as M±ME where

• M is the mean monthly CAT scans (2.08)
• ME is the margin of error

and margin of error (ME) around the mean can be found using the formula

ME=
`(t*s)/(√(N) )` where

• t is the corresponding statistic in the 95% confidence level (2.2)

• s is the standard deviation of the sample (0.15)

• N is the sample size (12)

Using the numbers ME=
`(2.2*0.15)/(√(12) )` ≈ 0.095

Confidence interval is then 2.08±0.095

(b) since the 95%confidence interval is higher than 1.95, the clinic outperforms.