109年 - 109 國立交通大學碩士班考試入學招生試題_運輸與物流班組聯招：統計學#121566

科目：研究所、轉學考(插大)◆統計學 | 年份：109年 | 選擇題數：0 | 申論題數：15

試卷資訊

所屬科目：研究所、轉學考(插大)◆統計學

選擇題 (0)

申論題 (15)

1. (總分 10 分) Suppose the records of a hotel show that, on the average, 10% of their prospective guests will not claim their reservation. If the hotel accepts 215 reservations and there are only 200 rooms in the hotel, what is the probability that all guests who arrive to claim a room will receive one?

(a). (7 分) If you consider the two reaction times as two independent random samples, do the data present sufficient evidence to indicate a difference in mean reaction times for the two reaction times? Calculate a 95% confidence interval for the difference in the two population means. Test using α = .05.

(b). (7 分) If you consider the two reaction times as paired observations, do the data present sufficient evidence to indicate a difference in mean reaction times for the two reaction times? Calculate a 95% confidence interval for the difference in the two population means. Test using α = .05.

(c). (11 分) Compare the results in (a) and (b), and discuss which experimental design is usually preferred? Which result is more theoretically sound? And what are the sources that affecting the widths of the confidence intervals? Explain.

(a). (5 分) Please first construct the sampling distribution of the average.

(b). (5 分) Find the approximate probabilities for an event where average duration exceeds 7 years.

(a). (5 分) First indicate the null and alternative hypotheses for this research question.

(b). (10 分) What is the sampling distribution of ? (Hint: probability distribution, mean, and standard error)

(c). (5 分) Interpret the obtained in (b).

(d). (5 分) Construct a 95% confidence interval to test whether the data present sufficient evidence to indicate that the midterm exam score is related to the final exam score (Hint: use 5% level of significance).

(e). (5 分) How do you describe the strength of the relationship between y and x? (Hint: calculate the correlation coefficient) 0.87

(f). (5 分) You are supposed to check the validity of the model by examining the residuals afterwards, what would you check? (Hint: think about the random error component specified)

(g). (5 分) For a student whose midterm exam score were 60, would you recommend the use of this model to predict his/her final exam score? Explain.

(a) (10 分) Use an appropriate method to determine whether or not a customer's preference is dependent on age.

(b) (5 分) Suppose you were a marketing expert, how would you advise Apple (hint: which age group you would target, or what further information they should collect for advanced analyses?)