假設某大學的經濟系與財管系的學生身高服從常態分配,自經濟系抽取25
位學生,其身高的標準差為4,而自財管系抽取20 位學生,其身高的標準
差為5,若信賴度為90%,請問兩系身高的離散狀況是否相同?(填入:
是或否)? (4) 。
某一學校的統計老師採用一個新的方案來教學,並宣稱在他的教學之下,
學生的統計考試平均成績至少為80 分以上,假設他有25 位學生,而學生
的統計成績的母體平均為75 分,母體標準差為2。請回答以下的2 個小題:
(1) 在這種情形下,型I 誤差是什麼? (7)
(2) 在5%顯著水準下,此套新的方法是否有效?(填入:是或否) (8)
The random variable Z follows a standard normal distribution. Please find
the probability P(−2.98 < Z < −1.54). (18)
Bank of America is curious about the grade level of people who use their ATM
at the Student Union. Freshmen and sophomores are classified as type A,
juniors and seniors as type B. Data are presented below for 48 people who used
the ATM during one Friday afternoon.
ABAAABBABBAABABAABBBBABB
AAABABAABBABBAAABBAABAAA
Test this sequence for randomness at the 5% significance level. What is the
statistic for this test? (19) Please decides whether this sequence is random
or not? (Yes or No) (20)
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