Statistical inference
refers to the process of drawing inferences about the sample based on the
characteristics of the population
is the same as descriptive statistics
is the process of drawing inferences about the population based on the information
taken from the sample
is the same as a census.
Given P(A) = 0.40 , P(B) = 0.60 , P(A∩ B) = 0.24 . Which of the following is true?
A and B are independent
A and B are not mutually exclusive
A and B are collectively exhaustive
None of the above.
Which of the following are characteristics of the normal probability distribution?
The mean, median, and mode are equal
The mean of the distribution can be negative, zero, or positive
The distribution is symmetrical
The standard deviation must be 1.
Which of the following statements are correct regarding the t-distribution?
t distribution approaches the standard normal curves as sample sizes become
large.
t test is quite robust.
t test is also referred to as the Student’s test.
All of above are correct
Which of the following statements about properties of point estimators are correct?
If the expected value of the sample statistic is equal to the population parameter
being estimated, the sample statistic is said to be an unbiased estimator of the
population parameter
The point estimator with the larger standard error is said to have less relative
efficiency than the other
A point estimator is said to be consistent if the values of the point estimator tend to
become closer to the population parameter as the sample size becomes larger
All of above are correct
Which of the following statements for Poisson distribution are correct?
The mean and variance of Poisson distribution are equal
The expected number of occurrences is not necessary to hold constant throughout
the experiment
As a rule of thumb, if n > 20 and np ≤ 7 , the approximation is close enough to
use the Poisson distribution for binominal problems
Each occurrence is independent of the other occurrences
Which of the following statements for Exponential distribution are not correct?
it is a family of distribution
it is a continuous distribution.
it describes random occurrences over some interval
it is skewed to the left.
The key difference between the binomial and hypergeometric distribution is that with
the hypergeometric distribution
the probability of success must be less than 0.5
the trials are independent of each other
the probability of success changes from trial to trial
the population is finite and known
Chebyshev’s Theorem is important because
it explains an unusual mathematical phenomenon
it enables us to give meaning to a sample standard deviation
it gives the fraction of the measurements in a sample that fall within k standard
deviation’s of the sample mean
it explains why the sample mean is a good measure of central tendency
Stratified sampling is generally more efficient than simple random sampling if:
only a few strata are used in the stratification
each strata contains about the same variability as the entire population with respect
to the characteristic of interest
non-sampling errors are of no consequence or expected to be slight
the item within each strata are relatively homogeneous.
台灣高鐵公司宣稱其台北至高雄列車的平均誤點不超過八分鐘,消基會懷疑高鐵
公司宣稱的真實性,因此決定調查其平均誤點時間,以作為統計檢定之用,請問
以下陳述何者正確。
型二誤差為列車誤點時間不超過八分鐘,但消基會認為列車誤點時間超過八分
鐘。
若雙方均同意以十二分鐘作為檢驗標準點,則增加調查班次數對雙方均有利。
若檢定出來之P 值很大,則對高鐵公司較有利。
以上皆非。
下列陳述何者正確
母體變異數未知,但已知母體為常態分配時,若用Z 分配與t 分配對母體平均
數計算信賴區間,則兩者信賴區間長度一樣。
母體為常態分配,且母體變異數為已知時,若信賴水準不變,則母體平均數的
信賴區間長度會隨樣本數的增加而變小。
信賴區間的長度會隨信賴水準的增加而變大。
以上皆非。
Which of the following statements for nonparametric statistics are not correct?
Nonparametric testes are usually not as widely available and well known as
parametric tests.
Nonparametric statistics are based in more assumptions about the population than
parametric statistics.
For small sample, the calculations for many nonparametric statistics can be tedious.
Probability statements obtained from most nonparametric tests are exact
probabilities.
When the smallest and the largest percentage of items are removed from a data set and
the mean is computed, the mean of the remaining data is:
the median
the mode
greater than the mean of the original data
less than the mean of the original data
none of the above are correct
A consumer test group wants to determine the difference in gasoline mileage of two
new developed hybrid car A and B . researchers took 50 cars for the car A and
also 50 cars for the car B , and tested each car on one tank of gas. The sample average
for the car A was 21.45 kilometer per litter (KM/L), with a standard deviation of 3.46
KM/L. The sample average for the car B was 24.6 KM/L, with a standard deviation
of 2.99 KM/L. Assume all samples are normal distribution. Construct a 95% confidence
interval to estimate the difference in the mean gas mileage between the car A and car
B . (4%)
The manager of a book store wants to determine what proportion of people who enter
the store use credit cards for their purchases. What size sample should he take so that at
98% confidence the error will not be more than 4%? (4%)
A book dealer received a lot of 1,500 books from a printer. The dealer plans to sample
12 books and use single-sample acceptance sampling to reach a decision about the lot.
If more than one book is defective, the dealer will reject the lot. Suppose the printer is
fairly certain that only 3% of the books are defective. What is the producer’s risk?
Suppose 12% of the lot of books is defective and that this rate would be too high for the
dealer to accept. what is the dealer’s risk in using this acceptance sampling? (4%)
A telephone survey conducted by a Research Company found that 43% of Taiwanese
expect to save more money next year than they saved last year because of the financial
crisis. 45% of those surveyed plan to reduce debt next year. Of those who expect to save
more money next year, 81% plan to reduce debt next year. A Taiwanese is selected
randomly. What is the probability that this person neither expect to save more money
next year nor plans to reduce debt next year? (4%)
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