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Answer:
a) (0.576, 0.624)
Step-by-step explanation:
Given that the sample proportion (p) = 60% = 0.6, sample size (n) = 900, confidence (C) = 85%
α = 1 - C = 1 - 0.85 = 0.15
α/2 = 0.075
The z score of α/2 (0.075) corresponds with the z score of 0.425 (0.5 - 0.075) which is equals to 1.44, hence
The margin of error (E) is:
The confidence interval = p ± E = 0.6 ± 0.024 = (0.576, 0.624)
First, illustrate the problem into a diagram like the one shown in the attached picture. The component vectors are shown in red (y-component) and blue (x-component). Since this is a right triangle, let's apply the trigonometric functions of sine and cos.
y-component, vy:
sin (π/3) = vy/8
vy = 6.928
x-component, vx:
cos (π/3) = vx/8
vx = 4
y-component, vy:
sin (π/3) = vy/8
vy = 6.928
x-component, vx:
cos (π/3) = vx/8
vx = 4