Question

A simple random sample of 16 observations is derived from a normally distributed population with a known standard deviation of 2.5. [You may find it useful to reference the z table.]

a. Is the condition that X− is normally distributed satisfied? Yes No

b. 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.)

c. Compute the margin of error with 90% 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?

The margin of error with 90% confidence.

The margin of error with 95% confidence.

Answer 1

Since n = 16 < 30 but population standard deviation is known thus, X follows normal distribution

b) n = 16  

= 2.5

margin of error with 95% confidence = (Z_/2)( / )  

= (1.96)(2.5/)  

= (1.96)(2.5/4)

= 4.9/4

= 1.225

c) Margin of error with 90% confidence =   (Z_/2)( / )  

= (1.65)(2.5/)  

= 4.125/4

= 1.03125

d) The margin of error with 95% confidence will lead to wider interval.