Question

1a. A medical stats class is interested in the mean pulse rate of "senior citizens". How many individuals are required to estimate the pulse rate with 99% confidence that the mean is within 2 beats per minute of the population mean. Based on 200 NIH data, assume a standard deviation of 12.5 beats per minute.  

b. Recent data suggests the standard deviation is closer to 17 bpm. How does a 99% CI with this standard deviation compare to (a) above?

Answer 1

Solution :

Given that,

a)

Population standard deviation = = 12.5

Margin of error = E = 2

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

sample size = n = (Z_/2* / E) ²

n = (2.576 * 12.5/ 2)²

n = 259.21

n = 260

Sample size = 260

b)

Population standard deviation = = 17

Margin of error = E = 2

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

sample size = n = (Z_/2* / E) ²

n = (2.576 * 17/ 2)²

n = 479.43

n = 480

Sample size = 480