111年 - 111 國立臺灣科技大學_碩士班招生試題：統計學(C)#120895

1. (20%) Consider the following frequency table of observations on the random variable X. Based on these 50 observations, is a binomial (二項) distribution with a number of trials (n)=6 and a probability of success (p)=0.25 an appropriate model? Perform a goodness-of-fit test (適合度檢定) with α=0.05.

2. (10%)Prove the mean and variance of the normal distribution N(μ, σ²) are μ and σ², respectively.

(a)Determine the probability of exactly one accident over a 2-month period.

(b)If fatalities (死亡) are involved in 20% of the accidents, what is the probability of fatalities occurring at this intersection over a period of 2 months? Assume that events of fatalities between accidents are statistically independent.

4. (10%)The following data are given:
Fit a polynomial (多項式) regression equation of the form

(a)Use a 0.1 level of significance.

(b)Use the P-value approach.

(a)Test the hypothesis that the mean is not 17.0, using the P-value approach.

(b)Find a 99% two-sided confidence interval on the mean.

111年 - 111 國立臺灣科技大學_碩士班招生試題：統計學(C)#120895

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