Question

A sample of heights of 115 American men yield a sample average of 58.67 inches. What would be the margin of error for a 99.74% CI of the average height of all such men if the population deviation is 2.9 inches? Round to the nearest hundredth

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 58.67

Population standard deviation =    = 2.9

Sample size = n =115

At 99.74% confidence level the z is ,

= 1 - 98% = 1 - 0.9974 = 0.0026

/ 2 = 0.0026/ 2 = 0.0013

Z_/2 = Z_0.0013 =3.01 ( Using z table    )

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

= 3.01 * ( 2.9 /  115 )

E= 0.81