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Answer:
a. The alternative hypothesis H₀: p'₁ ≠ p'₂ is accepted
b. Type I error
Step-by-step explanation:
Proportion of California residents who reported insufficient rest = 8.0%
Proportion of Oregon residents who reported insufficient rest = 8.8%
p'₁ = 0.08 * 11545 =923.6
p'₂ = 0.088 * 4691=412.81
σ₁ = =
= 29.15
σ₂ = =
= 19.40
Samples size of California residents n₁ = 11,545
Samples size of Oregon residents n₂ = 4,691
Hypothesis can be constructed thus
Let our null hypothesis be H ₀: p'₁ = p'₂
and alternative hypothesis H ₐ: p'₁ ≠ p'₂
Then we have
The test statistics can be computed by
t₀ = = 1104.83
c from tables is P(T ≤ c) = 1 - α where α = 5% and c = 1.65
since t₀ ≥ c then then the hypothesis is rejected which means the alternative hypothesis is rejected
b. Type I error, rejecting a true hypothesis