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Answer:
= 2.83
Reject H₀
Step-by-step explanation:
Hello!
The objective of the poll is to compare the proportions of people who believe in the theory of evolution. For this, the investigator took a sample of 1018 and divided it into two groups using a criteria their level in college education.
Group 1 (people with some college education)
n₁= 325
x₁= 133
sample proportion ^ρ₁=x₁/n₁ = 133/325 = 0.409
Group 2 (college graduates)
n₂= 228
x₂= 121
sample proportion ^ρ₂=x₂/n₂ = 121/228 = 0.531
pooled proportion ^ρ= 0.459
The statistic test that corresponds to test if the proportions are equal or different is the difference of population proportions and you have to use the normal approximation for the proportions to calculate it.
The hypothesis is:
H₀: ρ₂=ρ₁
H₁: ρ₂≠ρ₁
α: 0.10
Z=<u> (^ρ₂ - ^ρ₁) - (ρ₂ - ρ₁) </u> ≈ N (0;1)
√(^ρ(1 - ^ρ)*(1/n₂+1/n₁)
The critical region is two-tailed, so you have a lower critrical value and an upper critical value:
If ≤ -1.64 or if
≥ 1.64 you reject the null hypothesis.
If -1.64 < < 1.64, the you do not reject the null hypothesis.
Z=<u> (^ρ₂ - ^ρ₁) - (ρ₂ - ρ₁) </u> = <u> (0.531 - 0.409) - 0 </u> = 2.83
√(^ρ(1 - ^ρ)*(1/n₂+1/n₁) √(0.459(1 - 0.459)*(1/228+1/325)
= 2.83
Since the calculated Z value is greater than the upper critical value, the decision is to reject the null hypothesis. In other words, there is significative enough evidence to say that there is a difference between the population proportion of people who believe in the evolution theory and graduated from college and the population proportion of people who believe in the evolution theory and have some college education.
I hope it helps!