112年 - 112 國立臺北大學_碩士班一般入學考試試題_統計學系：統計學#147118

1. (10%) Use the researchers' data. Design a two-dimensional plot to display the association between weight and smoking status by cancer status. Explain your design.

2. (10%) Let \( X, W \), and \( Y \) be random variables representing smoking status, weight, and cancer status, respectively. Specify the three random variables by their sample spaces and distributions. Explain your notations and parameters.

(1) (5%) Write down a measure you would use to compare the weights between people of different cancer statuses.

(2) \( (5\%) \) Write down a measure you would use to help the researchers answer their question.

(1) \( (5\%) \) Calculate an estimate of your proposed measure in 3. (2).

(2) \( (10\%) \) Derive an approximate distribution of the estimator in 4. (1).

(3) \( (5\%) \) Comment and explain: how well the distribution you derive in 4. (2) approximates the exact distribution.

(1) \( (5\%) \) Determine the level of confidence used to construct the confidence interval.

(2) \( (5\%) \) If another random sample of 400 adults is taken, and 218 adults have tablets. To test the hypothesis if more than half of the adults in the city have tablets, what is the P-value and your conclusion?

(1) \( (5\%) \) Suppose the doctor would like to see if the data support that walking for one week will reduce the systolic blood pressure. What is the test statistics and your conclusion?

(2) \( (5\%) \) Construct a \( 95\% \) confidence interval for the reduction in systolic blood pressure.

(1) (5%) Determine the test statistics for the hypothesis: the absence is equally likely to occur on any of the five days.

(2) (5%) What is the critical value for testing the hypothesis above? What is your conclusion?

(1) (5%) To test if the average time spent watching TV is equal between male and female, what is the test statistics? Assume that the variance of time spent watching TV is equal for male and female.

(2) (5%) To test if the variance of time spent watching TV is equal for male and female, what is the test statistics and what is your conclusion?

(1) (5%) What is the sum of square between (among)?

(2) (5%) What is the test statistics for testing the hypothesis: there is no difference in sales of coffee beans for 4 different packaging? What is your conclusion?