Question

Among a sample of 16 people, the average heart rate was 69.0 beats per minute with a standard deviation 4.3 beats per minute. We are interested in the mean heart rate of the population. We assume that the heart rate is normally distributed, and that the population standard deviation is 4.8 beats per minute. At 95% confidence, what is the error bound?

Answer 1

Solution:

Given,

n = 16 ....... Sample size

= 69.0 ....... Sample mean

s = 4.3 ...sample Sd

Also ,

     = 4.8 ........Population standard deviation

Note that, Population standard deviation() is known..So we use z distribution.

Confidence level c = 95% = 0.95

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.05 2 = 0.025 and 1- /2 = 0.975

Search the probability 0.975 in the Z table and see corresponding z value

= 1.96   

Error Bound =

= Margin of error

= * ( / n )

= 1.96 * (4.8/16)

=  2.352