Please show your understanding of a Chi-square distribution with n degree of
freedom.
Suppose a firm has a plan to expand its size. Two options are currently available. The
first option is to double the size of its existing plant. The second option is to build a
replica of the existing plant at another location. Assume that the value of each
individual plant would be NT$100 million and the value of one plant if it were doubled
in size is NT$200 million. Further suppose that both locations are exposed to losses
from earthquakes. The probability of an earthquake at each location is 0.05.
Earthquakes at different locations are independent. A complete loss would occur if an
earthquake at either location happens.
What are the expected direct losses under the two options, respectively?
Suppose a firm has a plan to expand its size. Two options are currently available. The
first option is to double the size of its existing plant. The second option is to build a
replica of the existing plant at another location. Assume that the value of each
individual plant would be NT$100 million and the value of one plant if it were doubled
in size is NT$200 million. Further suppose that both locations are exposed to losses
from earthquakes. The probability of an earthquake at each location is 0.05.
Earthquakes at different locations are independent. A complete loss would occur if an
earthquake at either location happens.
We now assume that an indirect loss equal to NT$50 million only occurs if a
NT$200 million direct loss occurs. What are the expected indirect losses under the
two options, respectively?
Suppose fire insurance costs are uniformly distributed in Taiwan with a range of from
NT$200 to NT$1,182. What is the probability that a person’s annual cost for fire
insurance in Taiwan is between NT$410 and NT$825?
Assume that 18 big technology firms operate in Taiwan and that 12 are located in
Taiwan. If three technology firms are randomly selected from the entire list, what is the
probability that one or more of the selected companies are located in Tainan?
A margin of error is defined as how close the sample proportion is to the population
proportion. A prior study shows that 44% of 10,000 sampled undergraduate students
spend more than 3 hours a day surfing on the net. Suppose you would like to estimate
the proportion of undergraduate students who spend more than 3 hours a day surfing on
the net. How large a random sample would you need to estimate it to within a margin of
error of 0.05 with 95% confidence, if you use the abovementioned study as a guideline?
The following table shows a contingency table that crosstabulates student gender
(male/female) against exam result (pass/fail).
Calculate the Phi coefficient to test the strength of the relationship between student
gender and exam result.
The following table shows a contingency table that crosstabulates student gender
(male/female) against exam result (pass/fail).
Is the Pearson product-moment correlation coefficient applicable in this case?
Explain
A researcher wishes to estimate the difference in the average daily milk consumption of
whole milk drinkers and low-fat milk drinkers. He randomly selects 13 whole milk and
15 low-fat milk drinkers, and asks how many cups of milk per day they drink. The
average for the whole milk drinkers is 4.35 cups, with a standard deviation of 1.20 cups,
while the average for the low-fat milk drinkers is 6.84 cups, with a standard deviation of
1.42 cups. Assume that the daily consumption for the populations of whole and low-fat
drinkers is normally distributed. What is the 95% confidence interval of the difference
in the average daily milk consumption of the whole and low-fat milk populations?
Use data in the following table to find
the best-fitting linear relationship between the explanatory variable X and the
dependent variable Y , and
Use data in the following table to find
the coefficient of determination for this regression.
A study concludes that treating people appropriately for high blood pressure reduced
their overall mortality by 20%. Treating people adequately for hypertension has been
difficult, since it is estimated that 50% of hypertensives do not know they have high
blood pressure; 50% of those that do know are inadequately treated by their physicians;
and 50% that are appropriately treated fail to comply with this treatment by taking the
appropriate number of pills. What is the probability that among 10 true hypertensives at
least 50% are being treated appropriately and are complying with this treatment?
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