Question

A sample of size n=71 is drawn from a population whose standard deviation is u=15.

Part 1 of 2
(a) Find the margin of error for a 95% confidence interval for u. Round the answer to at least three decimal places.

The margin of error for a 95% confidence interval for u is?

Part 2 of 2
(b) If the confidence level were 90%, would the margin of error be larger or smaller?

(Larger/smaller), because the confidence level is (lower/higher).

Answer 1

Solution :

Given that,

(a)

Z_/2 = 1.96

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

= 1.96 * (15 / 71)

= 3.489

(b)

Z_/2 = 1.645

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

= 1.645 * (15 / 71)

= 2.928

smaller because the confidence level is lower