102年國立臺北大學企管所(甲組)統計學線上測驗

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3.: 何謂隨機變數(random variable)(5%)？請舉一個例子說明Gamma 分佈之隨機變數的意義？

4.: The Taipei Bus company has recently made a concerted effort to promote an image of reliability by encouraging its drivers to maintain consistent schedules. As a standard policy the company expects arrival times at various bus stops to have low variability. In terms of the variance of arrival times, the company standard specifies an arrival-time variance of 3 or less with arrival times measured in minutes. Periodically, the company collects arrival-time data at various bus stops to determine whether the variability guideline is being maintained. Assume that the variance of arrival time is within the company guidelines at significance of 5%. Assume that a random sample of 10 bus arrivals will be taken at a particular downtown intersection. Assume that the sample of arrival times for 10 buses shows a sample variance of 6.
Please write down the null hypothesis, the rejection rule and your conclusion.

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Graduate students in the Department of Business Administration sometimes do research by questionnaire survey or interviews which are costly, thus the number of questionnaire is crucial. Assume that your adviser asks you to conduct a survey of estimating the average amount spent on entertainment by each person visiting a popular resort. The people who plan the survey would like to be able to determine the average amount spent by all people visiting the resort to within $9.8, with 95% confidence. From past operation of the resort, an estimate of the population standard deviation is σ = 100 .

What is the minimum required sample size?

6.: You want to test for equality of five population means. First, what test should be your best choice? Second, please simply comment the using of two-sample t tests repeatedly in testing for equality of five population means? If the population distributions are highly skewed or otherwise different from normality, or if the population variances are not approximately equal, third, what test should be your best choice?

7.: The Neilsen Company, which issues television popularity rating reports, is interested in testing for differences in average viewer satisfaction with morning news, evening news, and late news. The company is also interested in determining whether differences exist in average viewer satisfaction with the three main networks: CBS, ABC, and NBC. Nine groups of 50 randomly chosen views are assigned to each combination cell CBS-morning, CBS-evening, …, NBC-late. The viewers’ satisfaction ratings are recorded. The Neilsen’s CEO is interested in following three questions: Are there differences in average satisfaction with three news time at 1% significance? Are there differences in average satisfaction in terms of three networks at 1% significance? Are there any interactions between some news time and some networks at 1% significance? Assume that the sum of squares of network, news time, interaction and error are 145, 160, 240 and 6200.
What is your conclusion to CEO’s last two questions?

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