One of the ANOVA assumptions is “homogeneity of variance”, please
answer: (14%)
(1) Please explain the meaning of “homogeneity of variance”.
(2) Why is it important? (4%)
(3) Please describe the procedure of performing the “Levene’s Test for
Homogeneity of Variance”. (6%)
Discuss the differences among the three measures of centrality.
The following questions are on the binomial distribution. (12%)
(1) Describe the conditions that could generate a binomial distribution.
(2) Generate a generalized equation for a binomial distribution. You have
to define the symbols in the equation in details. (4%)
(3) Find the expected value and the variance of the binomial distribution.
(2%)
(4) Draw a relative probability diagram to illustrate a sample with sample
size 5 and a binomial distribution which has a success probability of 0.5.
(4%)
Please answer the following questions. (8%)
(1) Compare a sample distribution with a sampling distribution. (4%)
(2) In case you are performing statistical inference on the expected value,
describe how to apply the CLM (central limit theorem) to either or both
of the above distributions.
Please answer the following questions. (8%)
(1) When you use grouped data of a sample (k groups, k > 4) with the
unknown population parameters to test the goodness of fit for a normal
distribution, how many degrees of freedom you are to suggest? Describe
the reason. (4%)
(2) In case you are performing statistical inference on the expected value
for a small-sized sample (e.g. a sample size of 10) with non-normal
distribution, you may use a signed test or a signed rank sum test.
Compare the two tests and make your suggestion.
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