110年 - 110 國立政治大學_碩士班招生考試_財務管理系:統計學#102897

Q1.(10%) Consider two events A and B, prove that if A and B are independent, then so are A^c and B^c.

(a) Find the probability that X lies between 3 and 10.

(b) Find the probability that X is less than 10

(c) Find the distribution function F(x) of X

(d) Find E(X) and V(X)

(a) What is the probability that a randomly selected Taiwan adult watches Tv for more than 5 hours?

(b) What is the number of hours below which only 10% of Taiwan adults watch TV per day?

(c) What is the probability that the average time watching TV by a random sample of 16 Taiwan adult is more than 5 hours?

(d) What is the probability that in a random sample of 10 Taiwan adults , at least one watch TV for more than 5 hours?

(a)Given that SSB=500, test at the 5% significance level to determine whether the treatment means differ?

(b) Given that SSB=500, test at the 5% significance level to determine whether the blocking is effective?

(c) Ignore blocking, test at the 5% significance level to determine whether the treatment means differ?

Q5.(15%) In simple linear regression, show that the test statistic for fortesting ρ=0, testing p = 0 is equivalent to the test statistic for testing β₁=0，where b₁ is the least square estimate of β₁, r is the sample correlation coefficient and is the estimated standard error of b₁.

(a) Estimate with 98% confidence the decrease in percentage support between now and 3 months ago.

(b) At the 5% significance level, can we infer that the national leader's popularity has decreased by more than 5%?

110年 - 110 國立政治大學_碩士班招生考試_財務管理系:統計學#102897

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