111年 - 111 國立臺北大學_碩士班一般入學考試試題_財政學系：統計學#147626

1. [15%] Calculate the interquartile range and standard deviation of the following sample data: 76, 64, 75, 68, 66, 74, 63, 72, 74, 66, 75, 78, 76, 67, 79, 75.

(a) Please find a \( 95\% \) confidence interval for \( \mu \).

(b) What do you mean when you say that a confidence coefficient is 0.95?

(c) What happens to the width of a confidence interval as the value of the confidence coefficient is decreased while the sample size is held fixed?

(a) What is the statistician's estimate of \( p \)?

(b) Approximately what sample size did the statistician use?

(a) Compute the least-squares point estimator of \( \alpha \) and \( \beta \).

(b) Compute the coefficient of determination.

(c) Calculate the variance estimates for \( \hat{\beta} \).

(d) With \( 10\% \) significance level, test the hypothesis " \( H_0: \sigma^2 = 1 \) . Explain your answer in details.

(a) Find the mean and variance of \( X \).

(b) Find the probability that no women are hired.

(c) Find the probability that 2 women and 1 man are hired.

6. [15%] Two groups of people are surveyed. In a sample of 55 drivers who are single people, they drive, on average, 79 miles per week for trips. In a sample of 70 married people, they drive, on average, 67 miles per week for trips. The sample standard deviations are 16 and 8 miles, respectively. At α = 0.01, can it be concluded that single people do more driving for trips than married people? Explain your answer in details.