The financial department at a large hospital would like to estimate the average

Question

The financial department at a large hospital would like to estimate the average outstanding balance owed by patients who have not paid their bills in full. In order for the interval to be useful in making budgeting decisions the department's management staff requires the the interval be no wider than $940 (total) at a confidence level of 95%. Ten files of patients carrying outstanding balances were randomly selected from a list of all of all pediatrics patients and the outstanding balance (rounded to the nearest integer) was recorded. The data are reported below in Table 1. This can be considered a pilot study.

A) The total number of patient records that must be sampled in order for the finance dept. management to meet their constraints of confidence level and bound is:

Table 1: Outstanding balances ($) for 10 randomly selected patients 5792 6464 5716 6845 4228 4705 5995 5851 9680 8401

Explanation / Answer

Getting the standard deviation of the sample,

s = 1627.801657

If the interval is no wider than 940, then the margin of error is 940/2 = 470.

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.025  
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
s = sample standard deviation =    1627.801657  
E = margin of error =    470  
      
Thus,      
      
n =    46.07904171  
      
Rounding up,      
      
n =    47   [ANSWER]

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