110年 - 110 國立清華大學碩士班考試入學試題_計量財務金融學系/甲組、乙組:統計學#105439

3. Let (-0.8-0.4,-0.2,0.6) be a sample from a uniform distribution on [-1,1]. Based on this sample, please generate (simulate) a sample which is from an exponential distribution .

4. Suppose that you're given statistics as below:

Assuming that the underlying populations have the same variances,
the P-value associated with the hypotheses H₀:μ₁=μ₂, H₁:μ₁＜μ₂ is
close to ______

5.Suppose that a matched-pairs design gave rise to the following data:

Assume that μ₁ and μ₂. are the corresponding population
means, and that the differences x₁-x₂. is approximately
normally distributed. At 90% confidence interval for μ₁-μ₂, is
given by (close to)______