110年 - 110 國立台灣海洋大學_碩士班招生考試_航運管理學系碩士班商業管理組：統計學#105329

科目：研究所、轉學考(插大)◆統計學 | 年份：110年 | 選擇題數：0 | 申論題數：26

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所屬科目：研究所、轉學考(插大)◆統計學

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申論題 (26)

a. At α = 0.1, does the data provide sufficient evidence to indicate that the standard deviations of two populations are different? (6%)

b. At α = 0.1, does the data provide sufficient evidence to indicate that the mean of population 1 is larger than the mean of population 2? (6%)

2. A journal surveyed its readers and asked how each rated the quality of management and the reputation of the company for over 250 worldwide corporations. Both the quality of management and the reputation of the company were rated on an excellent, good and fair categorical scale. Assume the sample data for 200 respondents below applies to this study.

Use a 0.05 level of significance and test for independence of the quality of management and the reputation of the company. (8%)

a. Construct an analysis of variance table to test whether there is a significant difference among the means of three treatments. (6%)

b. Use Fisher’s LSD approach to determine which populations have different means.

,where S_i is the sample standard deviation of treatment i, i =1, 2, 3. (6%)

a. Find the best-fitting line for the above data. (6%)

b. According to the information above, at a 0.05 level of significance, test for the claim “longer the years of experience, more the annual sales.”. (6%)

c. If the number of years of experience is 10 years, find the 95% confidence interval for the corresponding mean annual sales. (6%)

(a) Calculate and interpret the covariance between x and y. (3%)

(b) Calculate the coefficient of correlation, and comment on the relationship between x and y. (3%)

(c) Determine the least squares line, and use it to estimate the value of y for x = 6. (3%)

(d) Draw the scatter diagram and plot the least squares line. (3%)

(a) Calculate E(XY). (2%)

(b) Determine the marginal probability distributions of X and Y. (2%)

(c) Are X and Y independent? Explain. (2%)

(d) Calculate the expected values of X and Y. (3%)

(e) Calculate the variances of X and Y. (3%)

(f) Calculate COV(X,Y). (2%)

(g) Find the probability distribution of the random variable X + Y. (3%)

(h) Calculate E(X + Y) and V(X + Y) directly by using the probability distribution of X + Y. (3%)

a. What is the probability density function for this uniform distribution? (3%)

b. What is the probability that a patient would have to wait between one and two hours? (3%)

c. What is the probability that a patient would have to wait exactly one hour? (3%)

d. What is the probability that a patient would have to wait no more than one hour? (3%)

a. If a bank is selected at random from this distribution, what is the probability that the interest rate charged on a home loan exceeds 7.0%? (3%)

b. What is the most common interest rate? (3%)