Independent observations are a basic requirement for nearly all hypothesis test. Please
explain what it means and describe a situation that violates this assumption.
A correlation measures the degree of relation between two variables. Can we use the
correlation to (10%)
(一) use the value of one variable to predict the other?
(二) explain why the two variables are related?
Why or why not? Please explain and give one example respectively.
Please answer the following questions: (13%)
(一) What is the meaning of standard error of estimate? (3%)
(二) Given two variables X and Y , is there any relation between the correlation and
the standard error of estimate? Please explain why or why not. (5%)
(三) What is the meaning of “regression toward the mean”? Please give an example.(5%)
Suppose that n balls are tossed into b bins so that each ball is equally likely to fall
into any of the bins and that the tosses are independent. (8%)
(一) Find the probability that a particular ball lands in a specified bin.
(二) What is the expected number of balls tossed until a particular bin contains a ball?
A manufacturer of computer chips claims that less than 10% of his products are
defective. When 1,000 chips were drawn from a large production, 7.5% were found to
be defective. (10%)
(一) What is the population of interest?
(二) What is the sample?
(三) Does the value 10% refer to the parameter or to the statistic?
(四) Is the value 7.5% a parameter or a statistic?
(五) Explain briefly how the statistic can be used to make inferences about the
parameter to test the claim.
A space probe near Neptune communicates with Earth using bit strings. Suppose that is
its transmissions it sends a 1 one-third of the time and a 0 two-thirds of the time. When
a 0 is sent, the probability that it is received correctly is 0.9, and the probability that it is
received incorrectly (as a 1) is 0.1. When a 1 is sent, the probability that it is received
correctly is 0.8, and the probability that it is received incorrectly (as a 0) is 0.2. (8%)
(一) Find the probability that a 0 is received.
(二) Use Bayes’ Theorem to find the probability that a 0 was transmitted, given that a 0
was received.
Two vending machines, A and B , sell 280 ml-cans of coffee with the volume
normally-distributed. To examine the homogeneity of the products sold by the two
machines, 10 cans are drawn randomly with the standard deviation of 6 ml for the
volume of machine A , and 9 cans with 7 ml for machine B . (8%)
(一) Find 95% confidence interval for the standard deviation of the volumes of coffeefilled
cans for machine A .
(二) Find 95% confidence interval for the ratio of variances for the volumes of coffeefilled
cans for machine A to B .
There are 400 undergraduate students in the Department of Information Management in
a University. Out of the 400, 20 students have serious near-sighted problems. You
pickup 24 undergraduate students randomly. (9%) [Note: You need only state the
formula with the given data.]
(一) In case you draw a sample without replacement, what is the probability of 8
students with the serious near-sighted problems?
(二) In case you draw a sample with replacement, what is the probability of 8 students
with the serious near-sighted problems?
(三) Is it appropriate to adopt Poisson distribution to approximate the probability?
Describe the result in details.
可觀看題目詳解,並提供模擬測驗!(免費會員無法觀看研究所試題解答)