課程名稱︰生物統計學 課程性質︰必修 課程教師︰林曜松 開課學院：生科院 開課系所︰生科系 考試日期（年月日）︰2011/11/7 考試時限（分鐘）：原訂90分鐘 後來有延長一陣子 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : (一) Explain the following terms (30%) 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%) 所有需要查表的部份考題都有附 -- 對了、上校， ︵◢╱╲◣◢ ╱￣￣"╲ ╯╰ 你不會也吃過 ﹀ ▼◥ ╲▃ /◤◥◥ ∣ ︵ ︵ 惡魔果實吧？╲ ▇ ◥◥ ◢ ∥╲妳是想說我一碰到 /., ◥. ◤ ◥█ ◤╱ 水就變廢物是吧!? ▁▁ |/ 三︿ ￣ ∥/ \ φRISE ▆ == _________________/__﹀__________|__|__________________________________________ --

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