Question

A study of 40 physicians showed that they spent an average of 16.2 minutes per patient. Find the 95% confidence interval of the true mean for the average time spent with patients when the standard deviation = 3 minutes.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     =16.2

Population standard deviation =    = 3

Sample size n =40

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)

= 1.96 * (3 / 40 )

= 0.9297
At 95% confidence interval estimate of the population mean
is,

- E < < + E

16.2 -0.9297 <   <16.2 +0.9297

15.2703 <   < 17.1297

( 15.2703 ,17.1297 )