According to a statistics study, 9 of 199 males receiving medicine A and 13 of 97
males in the control group died within 12 months. Use the normal theory method to test
for significant differences in 12-month mortality between the two groups at the
significant level of 5%.
Refer to the previous question (Question 1). Perform the test using the contingency
table method using the Yates-corrected Chi-square statistic.
Show your understanding of the standardized normal distribution.
The predictive value positive of a screening test is defined as the probability that a
person has disease given that the test is positive. Suppose that 84% of hypertensives and
23% of normotensives are classified as hypertensive by an automated blood-pressure
machine. What is the predictive value positive of the machine, assuming that 20% of the
adult population is hypertensive?
The zero-order correlations among variables X , Y , and Z are displayed in the
following table.
Calculate the partial correlation coefficient that measures the relationship between
X and Y while controlling for Z .
The zero-order correlations among variables X , Y , and Z are displayed in the
following table.
Interpret the result you have obtained in (一).
Assume that random samples of male and female citizens have been selected, and each
person has been classified as being tall or short in terms of their height. The proportions
of male and females citizens are classified as being “tail” are 0.34 and 0.25 respectively.
The male sample and the female sample have 83 and 103 persons respectively. Is there
a statistically significant difference in the height (tall/short) by gender? Make a decision
at the significance level of 0.05.
It has been known that the results are not necessarily the same if bacteriuria is measured
on the same woman at two different points in time. Assume that 1/5 of all women who
are bacteriuric at time 0 are again bacteriuric at time 1 (one year later), whereas only
4.2% of women who were not bacteriuric at time 0 are bacteriuric at time 1. Let X be
the random variable representing the number of bacteriuric events over the two time
periods for one woman and still assume that the probability that a woman will be
positive for bacteriuria at any one exam is 5%. What is the probability distribution of
X ?
An insurer sells a policy to airline passengers for NT$1,000. If a passenger dies on a
given flight from a plane crash, the insurer will pay NT$1,000,000 to the chosen
beneficiary. Otherwise, there is no return. Suppose that passenger has about a 1 in a
million chance of dying on any given flight. You buy a policy for your next flight.
What is the probability distribution of the amount of money the beneficiary makes
from your policy?
An insurer sells a policy to airline passengers for NT$1,000. If a passenger dies on a
given flight from a plane crash, the insurer will pay NT$1,000,000 to the chosen
beneficiary. Otherwise, there is no return. Suppose that passenger has about a 1 in a
million chance of dying on any given flight. You buy a policy for your next flight.
Explain why the insurer is very likely to make a profit in the long run.
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