Mary and George go target shooting together. Both shoot at a target at the
same time. Suppose Mary hits the target with probability 0.4, whereas
George, independently, hits the target with probability 0.7.
(a) Given that exactly one shot the target, what is the probability that it
was Mary’s shot? (3%)
(b) Given that the target is hit, what is the probability the Mary hit it? (3%)
To estimate the difference between the mean ages of the two populations
( μ1 and μ2 , respectively) of Greenstone Department Store customers, a
simple of 10 inner-city customers and a simple random sample of 8
suburban customers were selected, with the following data:
瑕疵品比例一般不應該超過產品的20%,某位買主想要檢定一批產品瑕疵的比例
是否超過該限制。買主從該批產品隨機抽出100 件檢查,發現有25 件瑕疵品。
(a) 請寫出該檢定的虛無及對立假設。(3%)
(b) p-value 為何?(5%)
(c) 在α = 0.1下,買主該如何下結論?(3%)
(a) What is value of the sample correlation coefficient between X and Y?
(3%)
(b) Conduct an F-test of decide whether or not there is a linear relationship
between Y and X. State the alternatives, decision rule, and conclusion.
(α = 0.05 ) (7%)
(c) What range of R2 value are acceptable to conclude that there is linear
relationship? (α = 0.05 ) (5%)
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