課程名稱：統計學
課程性質：整開
課程範圍：ch7-10
開課教師：陳心蘋
開課學院：
開課系級：
考試日期(年月日)：99/01/14
考試時限(Mins)：2hrs
先聲明，這份試題的英文錯誤實在是有點多....
以下有變色的之後的是我找到比較明顯的錯誤
大家可以來一起抓錯誤~
試題本文：
1.(10%) In a population of 4000 employees, a simple random sample of 100
employees is selected in order to estimate the mean age for the population.
The population standard deviation is σ=7.2 years. What is the probability
that the sample mean age of the employees will be within(plus or minus)6.5
years of the population age?
2.(15%)An geneticist wishes to estimate the average weight of men for certain
race of people. If the population standard deviation is assumed to be 3
pounds and if she randomly samples 40 men.
a. Find the probability that the difference (缺between) the sample mean and
the true population mean will not exceed 0.7 pounds.
b. Suppose that the geneticist wants the difference (缺between) the sample
mean and the population mean to be less than 0.45 pounds, with the
probability 0.95. How many men should he sample to achieve this objective?
3.(15%) A random sample of 35 people employed by Florida state authority
established they earned an average wage (including benefits)
of ＄65.00 per hour. The sample standard deviation was ＄6.25 per hour.
a. Develop a 95 percent confidence interval for the population mean wage
(including benefits) for these employees.
b. How large a samole is needed to assess the population mean with an
allowable error of ＄1.50 at 99 percent confidence?
4.(10%) These are 2000 eligible voters in York County, South Carolina.
A random sample of 400 York County voters revealed 250 plan to vote to
return Louella Miller to the state senate. Construct a 99 percent confidence
interval for the proportion of voters in the county who plan for Ms. Miller.
5.(15%) Recent studies indicate that the typical 50-year-old woman spends
＄350 per year for personal-care products. The distribution of the amounts
spent follows a normal distribution with a stardard deviation of ＄45 per
year. We select a random samole of 20 women. The mean amount spent for
those sampled is ＄335.
a. What is the likelihood of finding a sample mean this(應該是is) large
or larger from(我覺得是than) the specified population?
b. Can we accept the result from recent studies at the 0.05 significance
level?
6.(10%) A recent survey of 50 executive who were laid off from their previous
position revealed it took a mean of 26 weeks for them to find another
position. The standard deviation of the sample was 6.2 weeks. Construct a
99 percent confident interval for the population mean.Is it reasonable that
the population mean is 28 weeks? Justify your answer.
7.(15%) Information from the American Institute of Insurance indicates the
mean amount of life insurance per household in the United States is
＄100,000. This distribution is positively skewed. The standard deviation
of the population is not known.
a.Suppose that you selected 50 samples of households. What is the expected
shape of the distribution of the sample mean?
b.Find the likelihood of selecting a sample with a mean of more than＄90,000
but less than＄102,000.2.(我總覺得這句文法有哪裡錯了)
8. One of the major U.S. tire makers wishes to review its warranty for their
rainmaker tire. The warranty is for 40,000 miles. The tire company believes
that the tire actually lasts more than 40,000 miles. A sample 49 tires
revealed that the mean number of miles is 45,000 miles with a standard
deviation of 15,000 miles. Test the hypothesis with a 0.05 significance
level. If the actual true tire mileage is 42,000 miles, what is the
probability of a Type II error?
※ 編輯: traintrain 來自: 118.168.88.156 (01/16 22:12)