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ijohnh14
06.03.2020 •
Mathematics
Exercise 6.22 provides data on sleep deprivation rates of Californians and Oregonians. The proportion of California residents who reported insufficient rest or sleep during each of the preceding 30 days is 8.0%, while this proportion is 8.8% for Oregon residents. These data are based on simple random samples of 11,545 California and 4,691 Oregon residents. (a) Conduct a hypothesis test to determine if these data provide strong evidence the rate of sleep deprivation is different for the two states. (Reminder: Check conditions) (b) It is possible the conclusion of the test in part (a) is incorrect. If this is the case, what type of error was made?
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Ответ:
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
Ответ: