所屬科目：研究所、轉學考(插大)◆生物統計學
1. Let X1, X2, ..., be a random sample drawn from an arbitrary distribution with afinite mean u and variance o . Which of the following statements about CentralLimit Theorem (CLT) are true? (Multiple choices, 10 marks)(A) As n - co, the sampling distribution of converges to the N(0, 1)distribution.(B)~ N(O, 1) for sufficiently large n.(C) If X is a Bin(n, p) random variable, then ~ N(O, 1).(D) Following , to apply the CLT, n must be at least 20 if p = 0.5.
(B) If the chance of accepting a batch of chemical that does not meet the standard is to be limited to no more than 1%, determine the critical value c so that H0 can be rejected if ＜ c, where & is the mean impurity level of 100 samples. (6 marks)
(C) If the measurements from one batch of the chemical had a sample mean of = 49.6 ppm of impurities, will H0 be rejected using a = 0.05? Also, write down the definition of the P-value and calculate it. (15 marks)
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be a random sample drawn from an arbitrary distribution with a
converges to the N(0, 1)distribution.(B)
~ N(O, 1) for sufficiently large n.(C) If X is a Bin(n, p) random variable, then 
~ N(O, 1).(D) Following 
, to apply the CLT, n must be at least 20 if p = 0.5.
＜ c, where & is the mean impurity level of 100
samples. (6 marks)
= 49.6 ppm of impurities, will H0 be rejected using a = 0.05? Also, write
down the definition of the P-value and calculate it. (15 marks)
