Question

If n=17, ¯ x x ¯ (x-bar)=41, and s=4, find the margin of error at a 99% confidence level. Give your answer to two decimal places.

Answer 1

Given,

X_bar = 41

n = 17

s = 4

Now calculate 99% confidence interval

CI = x_bar t*(s/n)

Df= n-1 = 17-1 = 16

t value for 99% confidence interval with 16 degrees of freedom is 2.921

​​​​​​Margin of error = ME = t*(s/n)

   ME = 2.921 *(4/17)

ME = 2.8338

Therefore CI = 41 2.8338

CI = 41 - 2.8338 and CI = 41 + 2.8338

CI = 38.17 and CI = 43.83

Therefore 99% confidence interval is

(38.17, 43.83).

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