a. Find the margin of error E. Solution (1) Given n=50, xbar=500, s=1 =0.05, Z(0

Question

a.    Find the margin of error E.

Explanation / Answer

(1) Given n=50, xbar=500, s=1 =0.05, Z(0.025)=1.96 (check normal table) (a) the margin of error E is Z*s/n = 1.96*(1/ sqrt(50)) =0.277 (b) The 95% CI is xbar ± Z*s/n --> 500 ± 0.277 --> ( 499.723, 500.277) ----------------------------------------------------------------------------------------------------------------------- (2) Given n=16, xbar=190, s=18 (a) the margin of error E is Z*s/n = 1.96*(18/ sqrt(16)) =8.82 (b) The 95% CI is xbar ± Z*s/n --> 190 ± 8.82 --> ( 181.18, 198.82) ----------------------------------------------------------------------------------------------------------------------- (3) Given n=100, p=64/100 = 0.64 (a) the margin of error E is Z*p*(1-p)/n =1.96*(sqrt(0.64*(1-0.64)/100)) = 0.094 (b) The 95% CI is p± Z*p*(1-p)/n --> 0.64 ± 0.094 --> ( 0.546, 0.734)

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