Knowing the null distribution of a hypothesis test and the decision rule allows one to
calculate the probability of type-I and type-II error. (7%)
For two nonzero probability events to be independent they must be based in two
different experiments. If not, they are dependent. (7%)
If the joint pdf of x, y is f (x, y) = kexy for 0 < x < 1 and 0 < x < 1, then x and y are
not independent. (7%)
Assume the random variable x: “number of people entering a bank within one hour” has
a Poisson distribution with λ = 4 . Then, the random variable y: “number of people
entering a bank within 30 minutes” has a Poisson distribution with λ = 2 . (7%)
Assume that the length (in days) of pregnancy (that is the time from impregnation to the
delivery of the child) is approximately normally distributed with μ = 260 and
σ 2 = 144 /α , where α is just a constant. A “potential” father is being sued for
paternity. He claims he is not the father, and argues that he was out of the country
during a period that began 275 days before the birth of the child and ended 245 days
before the birth of the child. Assume the judge is willing to declare he is not the father
only if there is at least 90% probability that the impregnation occurred during the period
where the “potential” father was out of the country. For which values of α will the
“potential” father be declare the legal father? Please also provide an intuitive
explanation for your result. (20%)
Assume that students’ GRE results are normally distributed with mean (μ ) 600 and
standard deviation 60. A new studying method (GRE+Plus) has been developed and its
authors claim that it improves the students’ performance in the GRE. Assume you have
data on the GRE score of 16 students that studied with GRE+Plus.
(一) Construct 5% test of the null hypothesis that the GRE+Plus method does not affect
the students’ performance against the alternative hypothesis that it improves their
performance. (15%)
(二) Explain, but do not compute, how your answer to part (一). Changes if you do not
know the variance of the population distribution. (5%)
可觀看題目詳解,並提供模擬測驗!(免費會員無法觀看研究所試題解答)