Answer:
We accept H₀ with 95 % of Confidence Interval we have enough evidence to conclude that the majority of members agree with the new system
Step-by-step explanation:
Sample size 800
Sample x₁ = 420 ( number of people in favor of a proposed scoring system), then
p₁ = 420/800 p₁ = 0,525 p₁ = 52,5 % then
q₁ = 1 - p₁ q₁ = 1 - 0,525 q₁ = 0,475
Sample size enought to use the approximation of the binomial didtribution to normal distribution
If significance level is 0,05 α = 0,05
and from z-table we look for z(c) ( z critical value)
z (c) = 1,64
Hypothesis Test:
Null Hypothesis H₀ p₁ = 0,5
Alternative Hypothesis Hₐ p₁ > 0,5
Alternative hypothesis tells us about a one tail-test to the right
To calculate
z(s) = ( p₁ - 0,5) / √ (p₁*q₁) / n
z(s) = 0,025 / √ 0,525*0,475/800
z(s) = 0,025 / √0,000311
z(s) = 0,025/0,01765
z(s) = 1,416
Comparing z(c) and z(s)
z(s) < z(c) 1,416 < 1,64
z(s) is in the acceptance region we accep H₀.
