106年 - 106 國立臺灣大學_碩士班招生考試：統計學(c)#122754

科目：研究所、轉學考(插大)◆統計學 | 年份：106年 | 選擇題數：0 | 申論題數：16

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選擇題 (0)

申論題 (16)

1. (10 points)A random sample of 20 students yielded a mean of = 72 and a variance of s² = 16 for scores on a college placement test in mathematics. Assuming the scores to be normally distributed, construct a 98% confidence interval for σ².

2. (10 points)Show that -1 ≤ ρ ≤ 1 where ρ is the coefficient of correlation.

(a)Assume the samples are paired.

(b)Assume the samples are not paired.

(c)The pairing of samples usually leads to smaller a CI. Explain why.

(a)Use the approach of hypothesis testing with α=0.10.

(b)Use P-value approach.

(a)E(X+Y)

(b)E(X-Y)

(c)E(XY)

(d)Var(2X-Y)

(e)Var(X+3Y-5)

(a)Determine the probability that a gap will be longer than 15 sec.

(b)What is the probability that the driver will cross at the fourth gap?

(c)Determine the mean number of gaps he has to wait until crossing the main street.

(d)What is the probability that he will cross within the first four gaps?