Question

A simple random sample of 11 observations is derived from a normally distributed population with a known standard deviation of 2.2. [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 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

a) Yes

The original distribution is normally distributed and hence, the sampling distribution will also be normally distributed

b) Margin of error = Z*

n = 11

= 2.2

For 95% Confidence level, Z* = 1.96

Margin of error = 1.96 x = 1.30

c) n = 11

= 2.2

For 95% Confidence level, Z* = 1.645

Margin of error = 1.645 x = 1.09

d) The margin of error with 95% confidence