Question

A simple random sample of 17 observations is derived from a normally distributed population with a known standard deviation of 3.5.

a. Is the condition that X−X− is normally distributed satisfied?
b. Compute the margin of error with 99% confidence. (Round intermediate calculations to at least 4 decimal places. Round "z" value to 3 decimal places and final answer to 2 decimal places.)
c. Compute the margin of error with 95% confidence. (Round intermediate calculations to at least 4 decimal places. Round "z" value to 3 decimal places and final answer to 2 decimal places.)
d. Which of the two margins of error will lead to a wider interval?

Answer 1

Solution :

(a)

Yes

(b)

Z_/2 = 2.576

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

= 2.576 * (3.5 / 17)

= 2.19

(c)

Z_/2 = 1.96

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

= 1.96 * (3.5 / 17)

= 1.66

d)

99% confidence interval is wider