Question

A simple random sample of 25 observations is derived from a normally distributed population with a known standard deviation of 8.2 (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 80% 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 of error 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.) Margin of error 1.03 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 80% confidence.

Answer 1

n=25 628.2 C=0.80 ) = )-C = 0,20 on = 0.1 Zal2 = 20.1=1, 282 - 1.282 x 8.2 525 2.1025 E = 2.10 C. C=0.80 2 = 0.10 >> Ş -0.05 Za12 à Zoos = 1.645 E=

= 1.645 4 8.2 vas = 2.6978 206 = 2.70 width of the confidence interval (w). W= 2E So w is directly proportional to margin of Enor. » Greater then margin of emor (E), more will be width of the interval. & Answer is The margin of error with gol. confidence.