109年 - 109 國立臺北大學_碩士班一般入學考試試題_財政學系：統計學#147783

(a) What is the probability that a female student studied abroad in 2019?

(b) What were the percentage of male undergraduate students in 2019?

(a) If a transcript from the sample includes the word "great", what is the probability that this speech is given by candidate A? Should your program label this transcript as candidate A's speech?

(b) Which of the two words, "economy" or "stupid", is a stronger indicator that the speech is given by candidate A? Why?

(a) Describe the sampling distribution of \( \bar{x} \). Develop a \( 90\% \) confidence interval for the average number of accidents.

(b) Is our estimator for the population mean unbiased? Briefly explain your answer.

(c) Is our estimator for the population mean consistent? Briefly explain your answer.

IV. (20%) A job seeker suspects that the salaries in his current city (A) is lower than the salaries in the neighboring city (B). The newspaper reported a recent survey on the salaries in these two cities with the following information:

Based on the information, can the job seeker conclude that the average salary in city A are lower than those in city B? Conduct a hypothesis testing with confidence level $\alpha = 0.05$ so that a rejection of the null hypothesis can provide us answer to the job seeker's question.

(a) What is the least squares regression model estimated by the researcher? What is the sample size?

(b) Is there a significant relationship between the two variables at the level of significance \( \alpha = 0.05 \)?

(c) Does the estimated regression provide a good fit? Explain your answer.