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Math 3080-001
Spring 2009
Worksheet #1
1.)
Name:_____________________________
An engineer has suggested changing a production process in the belief that it will
result in a reduced defective rate. Let p denote the true proportion of defective
items resulting from the changed process, and suppose that 5% of items produced
with the previous process were defective. Then the alternative hypothesis is the
assertion that ______________.
2.)
In our treatment of hypothesis testing, the __________ hypothesis will always be
stated as an equality claim.
3.)
The null hypothesis will be rejected if and only if the observed or computed
_____________ value falls in the ___________________.
4.)
A __________ error involves not rejecting the null hypothesis H o when H o is false.
5.)
A __________ error consists of rejecting the null hypothesis H o when H o is true.
6.)
The probabilities of type I and type II errors are traditionally denoted by the
Greek letters __________ and __________, respectively.
7.)
The rejection region is called ______________ if it consists only of large values
of the test statistic.
8.)
The rejection region is called ______________ if it consists only of small values
of the test statistic.
9.)
It is generally better to pose a hypothesis so that the __________ error is more
serious than the __________ error.
10.)
The value α that represents the probability of type I error is often referred to as
the __________ of the test.
11.)
For an upper-tailed z test, the level of significance α is just the area under the z
curve to the __________ of the critical value __________.
12.)
If the P-value is smaller than or equal to the level of significance α , then the
researcher should __________ at level α .
13.)
It is customary to call the data significant when the null hypothesis is
__________, and not significant otherwise.
14.)
If the P-value is larger than the level of significance α , then the researcher should
__________ at level α .
15.)
Suppose that when data from an experiment was analyzed, the P-value for testing
H o : µ = 100 versus H a : µ < 100
was calculated as .047. At the .01 level, H o would
______________.
16.)
Let
X 1 , X 2 ,KK , X m
be a random sample from a population with mean
µ1 and variance σ 12 , and let Y1 , Y2 ,KK , Yn
be
a
random
sample
with
mean
µ2 and variance σ 22 , and suppose that the X and Y samples are independent of one
another. The expected value of X − Y is __________ and the standard deviation
of X − Y is σ x − y = _____________.
17.)
In testing H o : µ1 − µ2 = 0 versus H a : µ1 − µ2 ≠ 0, the computed value of the test
statistic is z = 2.25. The P-value for this two-tailed test is then __________.
18.)
The number of degrees of freedom for a paired t test, where the data consists of n
independent pairs ( X 1 , Y2 ), ( X 2 , Y2 ),KK , ( X n , Yn ) is __________.
19.)
The
rejection
region
H o : µ D ≤ 0 versus H a : µ D > 0
for
level
.025
paired
t
test
in
testing
is __________, where the data consists of 12
independent pairs.
20.)
If X 1 and X 2 are independent __________ random variables with ν 1 and ν 2
degrees of freedom respectively, then the random variable F = ( X 1 /ν 1 ) /( X 2 /ν 2 )
has an F distribution.
21.)
Analogous to the notation tα ,ν and χα2 ,ν , we use Fα ,ν ,ν for the point on the axis that
1
2
captures __________ of the area under the F density curve with ν 1 and ν 2
degrees of freedom in the __________ tail.
22.)
F.95,6,10 = 1/__________ = __________ .
23.)
In a one-way ANOVA problem involving four populations or treatments, the null
hypothesis of interest is H o : __________ .
24.)
In one-factor ANOVA, both mean square for treatments (MSTr) and mean square
for error (MSE) are unbiased estimators for estimating the common
population variance σ 2 when ______________, but MSTr tends to overestimate
σ 2 when _______________.
25.)
In single-factor ANOVA, SST – SSTr = __________.
26.)
In one-factor ANOVA, __________ denoted by __________ measures the total
variation in the data that results from random error.
27.)
In one-factor ANOVA, __________ denoted by __________ is the part of total
variation that can be explained by possible differences in the population means.
28.)
Let F =MSTr/MSE be the test statistic in a single-factor ANOVA problem
involving four populations or treatments with a random sample of six
observations from each one.
When H o is true and the four population or
treatment distributions are all normal with the same variance σ 2 , then F has an F
distribution with degrees of freedom ν 1 = __________ and ν 2 = __________ . With f
denoting the computed value of F, the rejection region for level .05 test is
__________.