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

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