Find the margin of error for a poll, assuming that 95% confidence level and π = 0.5.(a) n = 50 (Round your answer to 4 decimal places.) Margin of error________.(b) n = 200 (Round your answer to 4 decimal places.) Margin of error________.(c) n = 500 (Round your answer to 4 decimal places.) Margin of error________.(d) n = 2,000 (Round your answer to 4 decimal places.) Margin of error________.

Answer:a. Margin of Error = 0.1386b. Margin of Error = 0.0694c. Margin of Error = 0.0439d. Margin of Error = 0.0220Step-by-step explanation:Margin of Error = Critical z Value * Standard ErrorFrom the formula, we need the critical z value to get our margin of errorTo get the critical value, we need the significance levelSignificance level =1 - confidenceSignificance level = 1 - 95%Significance level (SE)= 1 - 0.95 = 0.05Critical value = Z(SE/2)Critical value = Z(0.05/2)Critical value = Z(0.0025) = 1.96 ------------ From z table1. Givenn = 50π = 0.5First, we calculate the standard errorStandard Error (SE) = √(π)(1-π)/nFor n =50,SE = √0.5(1-0.5)/50 = √0.5*0.5/50= √0.005SE = 0.070711 (Approximated)SE = 0.071 (Approximated)Margin of Error = Critical value * standard errorMargin of Error = 1.96 * 0.070711Margin of Error = 0.138594Margin of Error = 0.1386 ---------- Approximated2. Givenn = 200π = 0.5First, we calculate the standard errorStandard Error (SE) = √(π)(1-π)/nSE = √0.5(1-0.5)/200 = √0.5*0.5/200= √0.00125SE = 0.0354 (Approximated)Margin of Error = Critical value * standard errorMargin of Error = 1.96 * 0.0354Margin of Error = 0.069384Margin of Error = 0.0694 ---------- Approximated3. Givenn = 500π = 0.5First, we calculate the standard errorStandard Error (SE) = √(π)(1-π)/nSE = √0.5(1-0.5)/500 = √0.5*0.5/500= √0.0005SE = 0.02236067977499789696409SE = 0.0224 (Approximated)Margin of Error = Critical value * standard errorMargin of Error = 1.96 * 0.0224Margin of Error = 0.043904Margin of Error = 0.0439 ---------- Approximated4. Givenn = 2000π = 0.5First, we calculate the standard errorStandard Error (SE) = √(π)(1-π)/nSE = √0.5(1-0.5)/2000 = √0.5*0.5/2000= √0.000125SE = 0.01118033988749894848204SE = 0.0112 (Approximated)Margin of Error = Critical value * standard errorMargin of Error = 1.96 * 0.0112Margin of Error = 0.021952Margin of Error = 0.0220 ---------- Approximated