課程名稱︰統計學 上
課程性質︰
課程教師︰雷立芬
開課學院：管院
開課系所︰國企系
考試日期（年月日）︰ 10/01/13
考試時限（分鐘）：3 hr
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.
a. Determine the sample size necessary to estimate a population mean to within
1 with 90% confidence given that the population standard deviation is 10 (5%)
b. Suppose that the sample mean was calculated as 150. Estimate the
population mean with 90% confidence.(5%)
2. Previous experience shows the mean and variance of a given process to be 45
and 36, respectively. Researchers are testing to determine whether these
values have changed. They gather the following dozen measurements of the
process. Assume the measurements are normally distributed.
a. Use these data and α=0.01 to test the hypothesis that population mean
is greater than 45.(16%)
b. Estimate with 95% confidence population mean. Explain the result.(7%)
c. Use these data and α=0.05 to test the hypothesis tha population
variance has changed.(10%)
d. Estimate with 99% confidence the population variance. Explain the
result. (7%)
52 44 51 58 48 49 38 49 50 42 55 51
3. Suppose a population is normally distributed as N(μ,36). We will conduct
a hypothesis test with: H0:μ≧20 versus H1:μ<20, where α=0.05, n=49.
a. Explain Type II error (4%)
b. What would bt the power of the test if the actual mean weere 19?(16%)
4. Suppose you are testinf H0: p=0.29 versus H1:p≠0.29. A random sample of
740 items show that 207 have this characteristic. With a 0.05 probability
of committing a type I error, test the hypothuesis.
a.Explain type I error(4%)
b.For the p-value method, what is the probability of the calculated Z
value for this problem? CAn you reject the null hypothesis? why?(8%)
c.If you had used the critical value method, what would the two critical
values be? Can you reject the null hypothesis? Why? (9%)
d.Estimate with 95% confidence the population propotion. Can you reject
the null hypothesis? Why (9%)
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