Question

A simple random sample of 11 observations is derived from a normally distributed population with a known standard deviation of 2.2 Compute the margin of error with 95% confidence Compute the margin of error with 90% confidence.

Answer 1

Answer: 7.1% and 6%.

Explanation:

Given data:

Sample size (n) = 11

Standard deviation = 2.2

Margin of error confidence level 95% = 1.96

Margin of error confidence level of 90% = 1.65

Solution:

P = 2.2/11

= 0.2.

ME = z √p (1-p)/n

at 95% interval

ME = 1.96 * √ 0.2 ( 1 – 0.2 ) / 11

= 1.96 * 0.03636

= 0.071.

= 7.1%

At 90% interval

ME = 1.65 * √ 0.2 ( 1 – 0.2 ) / 11

= 1.65 * 0.03636

= 0.06.

= 6%