課程名稱︰應用統計學一
課程性質︰政治學系三組必修
課程教師︰江瑞祥
開課學院：社會科學院
開課系所︰政治學系
考試日期（年月日）︰2008.01.18
考試時限（分鐘）：1:20 - 3:20 (120分鐘)
是否需發放獎勵金：是,謝謝
（如未明確表示，則不予發放）
試題 :
1.(15) According to an advertisement, a strain of soybeans planted on soil
prepared with a specified fertilizer treatment has a mean yield of 595
bushels per acre.Twenty-five farmers who belong to a cooperative plant
the soybeans in soil prepared as specified.Each uses a 40-acre plot and
records the mean yield per acre. The mean and variance for the sample of
25 farms are x-bar=563 and s^2 = 9790. Specify the null alternative
hypotheses used to determine if the mean yield for the soybeans is different
than advertised.
2.(10) We never conclude "Accept Ho" in a test of hypothesis.Why?
3.(20) It has been estimated that the G-car obtains a mean of 40 miles per
gallon on the highway,and the company that manufacture the car claims that
it exceed this estimate in highway driving.To support its assertion, the
company randomly selects 36 G-car and records the mileage obtained for each
car over a driving course similar to that used to obtain the estimate.
The following data resulted：x-bar=41.8 mile per gallon, s = 6 miles per
gallon.Calculate the power of the test if the true value of the mean is 41
miles per gallon. Use a value of α=.025
4.(10) A new apparatus has been devised to replace the needle in administering
vaccines.The apparatus, which is connected to a large supply of vaccine,can
be set to inject different amounts of the serum, but the variance in the
amount of serum injected to a given person must not be greater than 0.05 to
ensure proper inoculation. A random sample of 25 injections resulted in a
variance of 0.118. Specify the rejection region for the test.Use α=.10.
5.(5) Assume that (σ1)^2 = (σ2)^2 = σ^2 . Calculate the pooled estimator of
σ^2 for (s1)^2 = 0.88, (s2)^2 =1.01, n1 =10, n2 =12.
6.(25)The data for a random sample of five paired observations are shown below
Pair 1 2 3 4 5
-------------------------------------
Observation 1 3 4 3 2 5
Observation 2 5 4 4 5 6
(a) Calculate the difference between each pair of observations by
substracting observation 2 from observation 1. Use the differences to
calculate d and sd.
(b) Calulate the means x1-bar and x2-bar of each column of observations.
Show that d = (x1-bar) - (x2-bar)
(c) Form a 90% confidence interval for μD.
7. (15)An experiment has been conducted at a university to compare the mean
number of study hours expended per week by student athletes with the mean
number of hours expended by nonathletes.A random sample of 55 athletes
produced a mean equal to 20.6 hours studied per week and a standard
deviation equal to 5.9 hours.A second random sample of 200 nonathletes
produced a mean equal to 23.5 hours per week and a standard deviation equal
to 4.2 hours.How many students would need to be sampled in order to
estimate the difference in means to within 2.5 hours with probability 95%?
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