The Advanced e-Commerce Institute, Institute for Information Industry,
Taiwan, reported that 25% of online gamers were women. Assume that this
percentage was based on a sample of 400 gamers. If we want to estimate
the population proportion of online gamers who are women with a margin
of error of 0.03, the sample size should be taken is ______________. Use
95% confidence. (5%)
According to the Ministry of Transportation and Communications, Taiwan,
61% of Internet users connect their computers to the Internet by
Asymmetric Digital Subscriber Line (ADSL). Assume a population
proportion p = 0.61. The probability that a sample proportion from a
sample of 350 Internet users will be within ±0.05 of population
proportion is __________. (5%)
The National Association of Professional Baseball Leagues, Inc., reported
that attendance for 176 minor league baseball teams reached an all-time
high during the 2001 season. On a per-game basis, the mean attendance
for minor league baseball was 3530 people per game. Midway through the
2002 season, the president of the association asked for an attendance
report that would hopefully show that the mean attendance for 2002 was
exceeding the 2001 level. The hypotheses that could be used determine
whether the mean attendance per game in 2002 was greater than the
previous year’s level are __________. (2%) Assume that a sample of 92
minor league baseball games played during the first half of the 2002
season showed a mean attendance of 3740 people per game with a sample
deviation of 810. The p-value is __________. (4%)
A poker hand consists of 5 cars. If the cards have distinct consecutive
values and are not all of the same suit, we say that the hand is a “straight”.
For example, a hand consisting of the five of spades, six of spades, seven of
spades, eight of spades, and nine of hearts is a “straight”. Assume that all
possible poker hands are equally likely. The probability that one is dealt a
straight is __________. (6%)
A plane is missing, and it is presumed that it was equally likely to have
gone down in any of 3 possible regions. Let 1 − pi denote the probability
that the plane will be found upon a search of the i th region when the
plane is, in fact, in that region, i = 1, 2, 3. The conditional probability that
the plane is in region 1, given that a search of region 1 is unsuccessful, is
__________. (6%)
Let X be uniformly distributed over (0, 1). The probability density
function of Y = Xn is __________. (6%)
Suppose that the number of earthquakes occurring in Chia-Yi, Taiwan, in
any fixed interval of length t is a Poisson random variable with mean λ t .
The distribution function of the time, starting from now, until the next
earthquake is __________. (8%)
The game of craps is begun by rolling an ordinary pair of dice. If the sum of
the dice is 2, 3, or 12, the player loses. If it is 7 or 11, the player wins. If it
is any other number i , the player continues to roll the dice until the sum
is either 7 or i . If it is 7, the player loses; if it is i , the player wins. The
expectation of the number of rolls of the dice in a game of craps is ________.
(8%)
To compare with the fuel consumption of four different brands of
automobiles, we sampled each of them for five and obtained the following
data.
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)