A large χ 2 statistic tells us that there is strong association between two
categorical variables.
For data with a bell-shaped distribution, the inter-quartile range (IQR) is
usually larger than its standard deviation s .
For a survey sample to be representative, it is better for the sample size to
depends on the size of the population.
The elements in a sample space must be disjoint and with chance equally likely.
The White's test for heteroskedasticity can also be applied to test for model
specifications, in particularly against nonlinearities.
A die is rolled until the first time T that a five turns up.
(1) Find P(T > 3) . (5%)
(2) Find P(T > 6 |T > 3). (5%)
Suppose a professor at NCU has decided to use the following test for the final
of this term: Each student tosses a fair coin by her / himself to determine her /
his pass or failure for the statistics course. Calculate the size and power of this
test. (5%)
Historically a bank expects about 5% of its borrowers to default (i.e., not pay
back the money). The bank currently has 250 loans outstanding. The bank has
reserves on hand to cover losses if 25 of these loans were to default. Suppose
Jenny is using a binomial model to examine if these reserves be enough or not.
What must she assume about the behaviors of these borrowers? Do these
assumptions appear reasonable? (5%)
Let X ,Y be random numbers chosen independently from the interval [0,1]
with uniform distribution. Find the cumulative distribution and density of
Z =| X − Y | . (10%)
Explain the following terms. (1) Simpson's paradox; (2) survival bias. (10%)
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