110年 - 110 國立臺北大學_碩士班一般入學考試試題_統計學系：統計學#147385

一、(50%)

1. (20%) There are data sets of the heights (in inches) and weights (in pounds) of the members of a basketball team. Suppose the percentage of the heights of players between 68.6375 and 76.8625 is at least 36%, and the percentage of the weights of players between 170.14 and 205.52 is approximately 68%. Find the means and standard deviations of the heights and weights for this condition. Find the coefficients of variation of the heights and weights for each data set of the members of a basketball team. What assumptions and Theorems/ Rules do you apply to analyze these data sets? What can you conclude?

(a) \( (5\%) \) hypothesis testing,

(b) \( (5\%) \) confidence interval, and

(c) \( (5\%) \) \( p \) -value.

(d) \( (5\%) \) What procedures or assumptions do we need for this test?

(e) \( (5\%) \) How do we interpret the transition from the confidence level to the confidence coefficient in (b)?

(f) (5%) Accordingly, how do we apply the confidence interval for the estimation of the parameter in reality and explain the confidence?

二、填充題 (5% for each, 50% in total)

$$\chi{.10}^2(2) = 4.6052, \chi{.05}^2(2) = 5.991, \chi{.025}^2(2) = 7.3778, \chi{.01}^2(2) = 9.2103$$

1. As a company manager for NTPU Corporation there is a 0.40 probability that you will be promoted this year. There is a 0.72 probability that you will get a promotion, a raise, or both. The probability of getting a promotion and a raise is 0.25. What is the probability of getting a raise? (a) Are getting a raise and being promoted independent events? (Justify your answer) (b)

2. A group of 500 individuals were asked to cast their votes regarding a particular issue of the Equal Rights Amendment. We want to test to determine if the votes cast were independent of the sex of the individuals. The following table shows the results of the votes:

State the null and alternative hypotheses. __(c)__ Test the hypotheses using the p-value approach and at α=5%. What is your conclusion?__ (d)__

3. Define \( \triangle p \) as the daily change for the value of a portfolio in one day. Suppose that one-day volatility of \( \triangle p \) is 2 and \( \triangle p \) from one day to the next day are independent. The estimate of 4-day volatility for \( \triangle p \) is__ (e)__. Suppose that daily changes \( \triangle p \) have first-order correlation with 0.12. The 4-day volatility for \( \triangle p \) will be __(f)__.

4. A simple regression analysis was performed on a random sample, generating the following summary statistics SSx =250, SSy =700, SSxy =400, and n=14. The F-value for testing a significant relationship for simple regression analysis is __(g)__. What is the correlation coefficient between x and y? __(h)__.

5. An automobile dealer conducted a test to determine if the time in minutes needed to complete a minor engine tune-up depends on the five types of analyzers is used. Because tune-up time varies among three types of cars which were used as blocks in the experiment. The data were obtained: SST=430, SSTR=310, SSBL=85. The F-test value for testing any significant differences in the mean tune-up time among five analyzers is (i). If the block effect is ignored, the F-test value for testing any significant differences in the mean tune-up time among five analyzers for one-way ANOVA is__ (i)__