How do you solve?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 clinics follows

UkusakazaL

UkusakazaL

Answered question

2021-08-01

How do you solve?
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 clinics 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.
Find a two-sided 95% confidence interval for the standard deviation. What should you do to address any reservations about this confidence interval?
Round your answers to two decimal places (e.g. 98.76).
σ

Answer & Explanation

Ian Adams

Ian Adams

Skilled2021-08-17Added 163 answers

Step 1
Given the data, we can calculate the mean and s.d of the data.
x=Sum of all observationsTotal number of observations
=2.31+2.09+2.36+1.95+1.98+2.25+2.16+2.07+1.88+1.94+1.97+2.0212
=2.0816
Mean is 2.0816.
Standard deviation is given by.
s=x(xx)2n
=(2.312.0816)2+(2.092.0816)2..+(2.022.0816)212
=0.268912=0.1497
Step 2
With small samples, the interval of confidence interval is shown in below table.
n95%CI of SD20.45×SD31.9×SD30.52×SD6.29×SD50.60×SD2.87×SD100.69×SD1.83×SD250.78×SD1.39×SD500.84×SD1.25×SD
Our sample size is 12, we will go for 0.69×SD1.83×SD.
Range of 95% CI will given as.
0.69×SD1.83×SD
0.69×0.14971.83×0.1497
0.100.27
0.10σ0.27

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