A diagnostic test for a certain disease is not 100% reliable in that, if a person has the
disease the test will detect with probability 0.95. And, if a person does not have the
disease, the test will report that he or she does not have it with probability 0.98. Only
1% of the population has the disease in question. If a person is chosen at random from
the population and the diagnostic test indicates that he or she has the disease, what is the
conditional probability that he or she does, in face, have the disease? (10%)
Answer the following questions: (30%)
(一) What is pooled variance? Under what condition shall the pooled variance be used?(4%)
(二) What is the main purpose of matched sample design (compared to independent
sample design)? (4%)
(三) The sampling error is the absolute value of the difference between the value of an
unbiased point estimator and the value of the population parameter it estimates. But,
because the value of the population parameter is unknown, how will the sampling
error be measured? (8%)
(四) Is the statement “The joint probability of two events is the probability of the union
of these two events.” Correct? Please explain. (4%)
(五) What is the purpose of the power curve? (5%)
(六) What are the situations in which hypothesis testing procedures are commonly
employed? (5%)
Please explain the following terms in detail and state the relationship for each pair:
(12%)
(一) Standardized Residual vs. Studentized Deleted Residual
(二) Outlier vs. Influential Observation
(三) Autocorrelation vs. Multicollinearity
(四) Comparisonwise Type I Error Rate vs. Experimentwise Type I Error Rate
Consider a completely randomized design involving three treatment A , B , and C .
Instead of using ANOVA to compare the three means, multiple regression approach can
be used to deal with this problem. Please write a multiple regression equation and
define all variables to complete the analysis of hypothesis testing. (11%)
Please state the rationales for performing a (一) Parametric analysis, and (二)
Nonparametric analysis, i.e., under what situations, for what reasons, and with what
objectives, will we use them, and also state the pros and cons for both of the analyses.
(8%)
Please describe how to use χ2 test to perform both tests of (一) goodness of fits, and
(二) independence. You may use illustrative examples to clarify your descriptions.
(10%)
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