Answer:
z(s) is in the rejection zone , therefore we reject H₀
We have enough evidence to claim the proportion of individuals who attended college and believe in extraterrestrials is bigger than 37%
Step-by-step explanation:
We have a prortion test.
P₀ = 37 % P₀ = 0,37
sample size = n = 100
P sample proportion = P = 47 % P = 0,47
confidence interval 95 %
α = 0,05
One tail-test (right tail) our case is to show if sample give enough information to determine if proportion of individual who attended college is higher than the proportion found by Harper´s index.
1.-Hypothesis:
H₀ null hypothesis P₀ = 0,37
Hₐ alternative hypothesis P₀ > 0,37
2.-Confidence interval 95 %
α = 0,05 and z(c) = 1.64
3.-Compute of z(s)
z(s) = [ P - P₀ ] /√(P₀Q₀/n) ]
z(s) = [ ( 0,47 - 0,37 ) / √0.37*0,63/100
z(s) = 0,1 /√0,2331/100 ⇒ z(s) = 0,1 /0,048
z(s) = 2.08
4.-Compare z(s) and z(c)
z(s) > z(c) 2.08 > 1.64
5.-Decision:
z(s) is in the rejection zone , therefore we reject H₀
We have enough evidence to claim the proportion of individuals who attended college and believe in extraterrestrials is bigger than 37%
