Question

A simple random sample of 24 observations is derived from a normally distributed population with a known standard deviation of 7.8. [You may find it useful to reference the z table.]

a. Is the condition that X−X− is normally distributed satisfied?

• Yes

• No

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.)

Margin error: ?

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.)

Margin error: ?

d. Which of the two margins of error will lead to a wider interval?

• The margin of error with 95% confidence.

• The margin of error with 99% confidence.

Answer 1

Solution :

Given that,

a) yes,because sample size is less than 30.

b) Z$\alpha$/2 = Z_0.005 = 2.576

Margin of error = E = Z$\alpha$/2 * ( $\sigma$ /$\sqrt$n)

Margin of error = E = 2.576 * ( 7.8 /  $\sqrt$24 )

Margin of error = E = 4.10

c) Z$\alpha$/2 = Z_0.025 = 1.96

Margin of error = E = Z$\alpha$/2 * ( $\sigma$ /$\sqrt$n)

Margin of error = E = 1.96 * ( 7.8 /  $\sqrt$24 )

Margin of error = E = 3.12

d) The margin of error with 99% confidence