II. Essay (30%)
"Eye contact is a social signal." Do you agree or disagree with this statement? Write an essay of about 300 words to explain your reasons. Provide at least three examples to support your claim.
10. Let X₁, X₂, X₃, X₄ be independent random variables that have normal distributions N(μᵢ, σ²),
i = 1, 2, 3, 4. μi and σ² are the mean and variance of Xi. In order to test, at the α = 0.05 significance
level, the hypothesis H₀: μ₁ = μ₂ = μ₃ = μ₄ = μ against all alternatives on the basis of a random
sample of size nᵢ = 3 from each of the four distributions. Determine whether we accept or reject H₀ if
the observed values from the four distributions are, respectively, as follows:
9. When a certain method is used to collect a fixed volume of rock samples in a region, there are four resulting rock types. Let X₁, X₂, and X₃ denote the proportion by volume of rock types 1, 2, and 3 in a randomly selected sample (the proportion of rock type 4 is 1-X₁-X₂-X₃, so a variable X₄ would
be redundant). If the joint probability density function (pdf) of X₁, X₂, X₃ is
(b) Find the probability that rocks of types 1 and 2 together account for at most 50% of the sample. (5%)
80. 下列何者是針對學齡兒童所定出的最優先牙病防治順序?
(A)緊急照顧(如急性蜂窩組織炎之感染控制)
(B)緊急事故之預防(如牙齒折斷或脫落之防護套)
(C)齲齒治療
(D)口腔炎之預防
79. 統計學中的「第一類型的錯誤(type I error)」是指:
(A)錯誤地接受虛無假說的機率
(B)錯誤地推翻虛無假說的機率
(C)正確地接受虛無假說的機率
(D)正確地推翻虛無假說的機率
78. 針對國小一、二年級之學童,口腔健康教育應以下列那一種方式為主要內容?
(A)良好口腔清潔習慣的養成
(B)對齲齒、牙周病、口腔癌等疾病有初步的了解
(C)對自己身體與牙齒之認識
(D)對各種口腔疾病之預防有一定的認知
This is a large modal.