94年 - 94 國立交通大學管碩士班考試入學試題_運輸科技與管理學系：統計學#124803

(a) Chebyshev inequality

(b) P-value

(c) Trimmed mean

(d) Wilcoxon signed rank test

(a) (5%) A hospital administrator wants to find out if the single parents working in the hospital have a higher rate of absenteeism than parents who are not single.

(b) (5%) A researcher would like to assess the extent of pilferage in the materials storage warehouses of manufacturing firms on the Kaohsiung Port.

(c) (5%) The director of human resources wants to investigate the relationship between drug abuse and dysfunctional behavior among blue-color workers in a particular plant.

(d) (5%) A gun manufacturing firm would like to know the types of guns possessed by various age groups in New York City.

(a) (5%) Obtain the mean and the standard deviation of the sampling distribution of .

(b) (10%) Using a normal approximation, find the probability that (1)is less than 0.35；(2) lies within ±0.05 of the population proportion p.

(c) (5%) Calculate the interval in part (b)-(2) for a sample of size 1000. What is the effect of the larger sample size?

(a) (10%) Test whether opinion and gender of viewer are independent, control the α risk at 0.10. State the alternatives, the decision rule, the value of the test statistic, and the conclusion.

(b) (5%) Given the conclusion in part (a), should the next step be to examine the relative squared residuals for the test? Explain.

5. (10%) The chi-square test statistic X² is based on a comparison of the sample frequencies
f_i with the corresponding expected frequencies F_iunder the null hypothesis H₀. Show that test statisticcan be written as the following weighted sum of the residuals f_i - F_i, that is

(a) (5%) Use the t ratio to test the hypothesis that X is a statistically significant variable.

(b) (5%) Determine the estimated standard deviations of the parameter estimators.

(c) (5%) Construct a 95 percent confidence interval for the coefficient of X. Does this interval include zero?