Question

A sample of size n equals 76 is drawn from a population whose standard deviation is o equals 27

A) Find the margin of error for a 99% confidence interval for U. Round the answer to at least three decimal places.

B) if the confidence level were 95%, would the margin of error be larger or smaller?

_______ because the confidence level is _______

Answer 1

Solution :

Given that,

Population standard deviation =    = 27
Sample size = n =76

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576   ( Using z table )

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

= 2.576 * (27 / 76)

E= 7.978

(B)

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 * (27 / 76)

E= 6.070

confidence level were 95%, would the margin of error be smaller