Answer:
The margin of error M.O.E = 2.5%
Step-by-step explanation:
Given that;
The sample size = 1500
The sample proportion [tex]\hat p[/tex] = 0.60
Confidencce interval = 0.95
The level of significance ∝ = 1 - C.I
= 1 - 0.95
= 0.05
The critical value:
[tex]Z_{\alpha/2} = Z_{0.05/2} \\ \\ Z_{0.025} = 1.96[/tex] (From the z tables)
The margin of error is calculated by using the formula:
[tex]M.O.E = Z_{\alpha/2} \times \sqrt{\dfrac{\hat p(1 -\hat p)}{n}}[/tex]
[tex]M.O.E = 1.96 \times \sqrt{\dfrac{\hat 0.60(1 -0.60)}{1500}}[/tex]
[tex]M.O.E = 1.96 \times \sqrt{\dfrac{0.24}{1500}}[/tex]
[tex]M.O.E = 1.96 \times \sqrt{1.6 \times 10^{-4}}[/tex]
M.O.E = 0.02479
M.O.E ≅ 0.025
The margin of error M.O.E = 2.5%
