The U.S. Bureau of Labor Statistics collects information of the ages of people in the
civilian labor, force and publishes the results in Employment and Earnings. Thirty-six
people in the civilian labor force are randomly selected; the sample mean and the
population standard deviation of the ages are 36 years and 12 years, respectively.
Answer the following questions:
(1) Find a 95% confidence interval for the mean age of all people in the civilian labor
force. (4%)
(2) Determine the sample size needed in order to be 95% confident that population
mean is within 1 year of the sample mean. (4%)
請列出以下幾種函數的機率密度函數,並詳細推導它們的動差母函數(無過程不
給分):
(1) 常態分配。(6%)
(2) 二項分配。(6%)
(3) 指數分配。(6%)
(以上分配所需之參數請以下列符號表示:μ 表示平均數,σ 2 表示變異數,n表
示實驗次數, p 表示成功機率)
An interval estimate is a range of values used to estimate
the shape of the population's distribution
the sampling distribution
a sample statistic
a population parameter
In a questionnaire, respondents are asked to mark their gender as male or female.
Gender is an example of a
qualitative variable
quantitative variable
qualitative or quantitative variable, depending on how the respondents answered the
question
None of these alternatives is correct.
The total number of data items with a value less than the upper limit for the class is
given by the
frequency distribution
relative frequency distribution
cumulative frequency distribution
cumulative relative frequency distribution
When data are positively skewed, the mean will usually be
greater than the median
smaller than the median
equal to the median
positive
Bayes' theorem is used to compute
the prior probabilities
the union of events
intersection of events
the posterior probabilities
A probability distribution showing the probability of x successes in n trials, where the
probability of success does not change from trial to trial, is termed a
uniform probability distribution
binomial probability distribution
hypergeometric probability distribution
normal probability distribution
Which of the following is not a characteristic of the normal probability distribution?
The mean, median, and the mode are equal
The mean of the distribution can be negative, zero, or positive
The distribution is symmetrical
The standard deviation must be 1
Stratified random sampling is a method of selecting a sample in which
the sample is first divided into strata, and then random samples are taken from each
stratum
various strata are selected from the sample
the population is first divided into strata, and then random samples are drawn from
each stratum
None of these alternatives is correct.
A goodness of fit test is always conducted as a
lower-tail test
upper-tail test
middle test
None of these alternatives is correct
An experimental design where the experimental units are randomly assigned to the
treatments is known as
factor block design
random factor design
completely randomized design
None of these alternatives is correct
A sample of 200 elements from a population is selected, and the standard deviation of
the sample is computed. For an interval estimation of μ , the proper distribution to use
is the
normal distribution
t distribution with 200 degrees of freedom
t distribution with 201 degrees of freedom
t distribution with 202 degrees of freedom
The ANOVA procedure is a statistical approach for determining whether or not
the means of more than two samples are equal
the means of two or more samples are equal
the means of two samples are equal
the means of two or more populations are equal
We are interested in testing whether the variance of a population is significantly less
than 1.44. The null hypothesis for this test is
Ho :σ 2 < 1.44
Ho : s2 ≥ 1.44
Ho :σ ≤ 1.20
Ho :σ 2 ≥ 1.44
If we are interested in testing whether the proportion of items in population 1 is larger
than the proportion of items in population 2, the
null hypothesis should state P1− P2 < 0
null hypothesis should state P1− P2 ≥ 0
alternative hypothesis should state P1− P2 > 0
alternative hypothesis should state P1− P2 < 0
To compute an interval estimate for the difference between the means of two
populations, the t distribution
is restricted to small sample situations
is not restricted to small sample situations
can be applied when the populations have equal means
None of these alternatives is correct
Fowle Marketing Research, Inc., bases charges to a client on the assumption that
telephone surveys can be completed in a mean time of 15 minutes or less. If a longer
mean survey time is necessary, a premium rate is charged. Suppose a sample of 100
surveys shows a sample mean of 18 minutes. Use σ = 5 minutes. Is the premium rate
justified?
(1) Formulate the null and alternative hypotheses for this application. (3%)
(2) Compute the value of the test statistic. (3%)
(3) At α = .01 , what is your conclusion? (4%)
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