Question

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 1

Answer:

a. Margin of Error = 0.1386

b. Margin of Error = 0.0694

c. Margin of Error = 0.0439

d. Margin of Error = 0.0220

Step-by-step explanation:

Margin of Error = Critical z Value * Standard Error

From the formula, we need the critical z value to get our margin of error

To get the critical value, we need the significance level

Significance level =1 - confidence

Significance level = 1 - 95%

Significance level (SE)= 1 - 0.95 = 0.05

Critical value = Z(SE/2)

Critical value = Z(0.05/2)

Critical value = Z(0.0025) = 1.96 ------------ From z table

1. Given

n = 50

π = 0.5

First, we calculate the standard error

Standard Error (SE) = √(π)(1-π)/n

For n =50,

SE = √0.5(1-0.5)/50

= √0.5*0.5/50

= √0.005

SE = 0.070711 (Approximated)

SE = 0.071 (Approximated)

Margin of Error = Critical value * standard error

Margin of Error = 1.96 * 0.070711

Margin of Error = 0.138594

Margin of Error = 0.1386 ---------- Approximated

2. Given

n = 200

π = 0.5

First, we calculate the standard error

Standard Error (SE) = √(π)(1-π)/n

SE = √0.5(1-0.5)/200

= √0.5*0.5/200

= √0.00125

SE = 0.0354 (Approximated)

Margin of Error = Critical value * standard error

Margin of Error = 1.96 * 0.0354

Margin of Error = 0.069384

Margin of Error = 0.0694 ---------- Approximated

3. Given

n = 500

π = 0.5

First, we calculate the standard error

Standard Error (SE) = √(π)(1-π)/n

SE = √0.5(1-0.5)/500

= √0.5*0.5/500

= √0.0005

SE = 0.02236067977499789696409

SE = 0.0224 (Approximated)

Margin of Error = Critical value * standard error

Margin of Error = 1.96 * 0.0224

Margin of Error = 0.043904

Margin of Error = 0.0439 ---------- Approximated

4. Given

n = 2000

π = 0.5

First, we calculate the standard error

Standard Error (SE) = √(π)(1-π)/n

SE = √0.5(1-0.5)/2000

= √0.5*0.5/2000

= √0.000125

SE = 0.01118033988749894848204

SE = 0.0112 (Approximated)

Margin of Error = Critical value * standard error

Margin of Error = 1.96 * 0.0112

Margin of Error = 0.021952

Margin of Error = 0.0220 ---------- Approximated