Answer:
We fail to reject the null hypothesis, we accept H₀
Step-by-step explanation:
Population proportion p₀ = 55 % p₀ = 0,55
Sample size n = 280
Sample mean p = 51 % p = 0,51 q = 0,49
n*p and n*q are both bigger than 10 therefore we can approximate the binomial distribution to a normal distribution
Test Hypothesis
Null Hypothesis H₀ p = p₀
Alternative Hypothesis Hₐ p ≠ p₀
Significance level is α = 0,05 but we have a two-tail test then
α/2 = 0,025
z(c) = - 1,96
Computing z(s)
z(s) = ( p - p₀ ) / √(p*q)/n
z(s) = ( 0,51 - 0,55 ) / √(0,51*0,49)/280
z(s) = - 0,04 * 16,73 / 0,5
z(s) = - 1,34
Comparing
z(s) and z(c)
- 1,34 < - 1,96
| z(s) | < | z(c)|
Then z(s) is in the acceptance region, we accept H₀
