103年 - 103 國立交通大學管碩士班考試入學試題：統計學#123989

1. (10%) Please present the figures with symmetric, right-skewed and left-skewed distribution respectively, and indicate the relative locations of mean, median and mode under such three types of distribution.

(a) What criteria are used to select a better estimator? (3%)

(b) What is the Type I (α Type) error? (3%)

(c) What parameters are required to specify an F-distribution function? (3%)

(d) What are the expectation value and variance for the random variable following the Chi-square () distribution with k degrees of freedom? (3%)

(e) What is the simple random sampling? (3%)

3. (10%) When the production process is functioning correctly, which is 90% of the time, 10% of all bulbs produced are defective. However, the process is susceptible to an occasional malfunction, leading to a defective rate of 50%. If a defective bulb is found, what is the probability that the process is functioning correctly? If a non-defective bulb is found, what is the probability that the process is operating correctly?

4. (10%) A random sample of 100 people shows that 25 are left-handed. Please form a 95% confidence interval for the true proportion of left-handers

(6%) (a) the sample mean x̄ = is an unbiased estimator of the population mean μ, and

(9%) (b) the sample variance s² = is an unbiased estimator of the population variance σ².

(a) Can the company conclude that Provider A is better than Provider B at a 5% level of significance? (10%)

(b) Will the results stay the same at the 1% level of significance? (5%)

7. (10%) University administrators have collected the following information concerning student grade point average (GPA) and the school of the student's major. Determine if there is any association between GPA and major at α = 0.05.

(a) Construct the two-way analysis of variance table. (9%)

(b) Test the null hypotheses that population mean sales are the same for all three types of soups and for all four quarters at α = 0.05. (6%)