# The sample proportion of Americans who are dissatisfied with education in kindergarten through grade 12 is 0.55 with sample of size 1000. We are interested in testing at the 5% significance level, if this sample provides evidence that the proportion of Americans who are dissatisfied with education in kindergarten through grade 12 differs significantly from 50%. Required: What is the p-value?

###### Question:

Required:

What is the p-value?

## Answers

Answer: p-value = 0,000755We reject H₀. We can support that Americans who are dissatisfied with education in kindergarten throug grade 12 differs significantly from 50%Step-by-step explanation:Sample proportion : p₁ = 0,55Sample size n = 1000q₁ = 1 - p₁ q₁ = 1 - 0,55 q₁ = 0,45Hypothesis Test:Null Hypothesis H₀ p₁ = 0,5 ( 50 % )Alternative Hypothesis Hₐ p₁ ≠ 0,5Alternative hypothesis indicates that we have to develop a two-tail testas n = 1000p₁*n = 0,55 * 1000 = 550 q₁*n = 0,45*1000 = 450Both products are bigger than 5. We can use the approximation of binomial distribution to normal distribution.Significance level α = 5% α = 0,05 and α/2 = 0,025z(s) = ( p₁ - 0,5 ) / √p₁*q₁/1000z(s) = 0,05 * 31,62 / 0,4974z(s) = 3,1785From z-table we find p-value = 0,000755Therefore p-value < 0,025We are in the rejection region, we reject H₀