1) Median
2) Precision
3) p-values
4) Power of the test
5) Independent events
6) Unbiased estimator
7) Central limit theorem
8) Significant level
9) Conditional probability
10) Standard error of the mean
(二) From a certain population of tilapia, a sample of 30 fish was
dissected to determine the number of dorsal spine (Xi) in each.
The data collected are summarized in the table.
========================
fi 2 14 8 6
Xi 8 9 10 11
========================
Calculate the (a) mean,
(b) median,
(c) standard deviation for this data set. (5%)
(三) Each year the density of 8 species of Odonata (dragonflies and
damselflies) is monitored in a wetland preserve. If the density
of each species is to be compared with the density of every other
species, how many comparisons must be made? (5%)
(四) A large fruit-eating bat called the black flying fox, Pleropus
alceto, occupies a large mangrove swamp on Indooroopilly Island.
Assume that about 70% of these bats are infected with an
ectoparasitic mite and 40% have larger tick parasites. Twenty
percent are infected with both.
(a) Find the probability that a randomly chosen bat will have
some parasites.
(b) If a randomly chosen bat has mites, what is the probability
that it will not have ticks?
(c) Are the presence of the two types of ectoparasites
independent of each other? (10%)
(五) To determine the frequency of type O blood (the universal donor)
in a population, a random sample of 400 people were blood typed
for the ABO group. Of this 400, 144 were found to be type O. Use
the Central Limit Theorem and the normal approximqation of the
binomial to calculate the 90% confidence limits for the proportion
of the population that has type O blood. (10%)
(六) Let's claim that a population is normally distributed with a mean μ
of 20 and a standard deviation σ of 12 or it is normally distributed
with a mean μ of 24 and a standard deviation σ of 12. We don't know
which of these populations we are sampling, but it is one or the other.
If we take a sample of sinze n=36, α=0.05 as the probability of a
Type I error, and use hypothese Ho: μ=20, σ=12, Ha: μ=24, σ=12.
Please calculate the probability β of Type II error. (15%)
(七) As part of a benthic community survey of Lady Elliot Island, nine sea
stars, Linckia laevigata, were collected and their longest arm was
measured to the nearest tenth of a centimeter. Assure normality for
this polulation.
=========================================
7, 10, 10, 11, 11, 11, 12, 13, 14
=========================================
(a) Calculate the 95% confidence interval for the polulation mean.
(b) Calculate the 95% confidence interval for the polulation variance.
(c) Determine whether the mean is significantly different from 13 cm
(α=0.05). (15%)
(八) Abuse of substance containing toluene can produce neurological symptoms.
In an investigation of the mechanism of these toxic effects, researchers
measured the concentrations of certain chemicals in the brains of rats
who had been exposed to a toluene-laden atmosphere. The concentrations
(ng/gm) of the brain chemical norepinephrine(NE) in the medulla region
of brain of 9 toluene-exposed rats was determined and recorded below.
Does the exposure to toluene significantly increase NE levels in rats
above the normal average of 10 ng/gm with α=0.05?
=========================================
5, 7, 9, 12, 14, 40, 50, 60, 64
=========================================
(a) Please use the one-sample t-test method
(b) Please use the one-sample Wilcoxon sighed-rank test method. (10%)
