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
