Question

A chi-square test for goodness of fit is used to examine the distribution of individuals across four categories, and a chi-square test for independence is used to examine the distribution of individuals across the six categories in a 2×3 matrix of categories. Which test has the larger value for df?

a. The test for goodness of fit

b. Both tests have the same df value.

c. The test for independence

d. The df value depends on the sizes of the samples that are used.

Answer #1

For each of the following examples, state whether the chi-square
goodness-of-fit test or the chi-square test for independence is
appropriate, and state the degrees of freedom (df) for the
test.
Part (a)
A student tests whether the professor's speaking style (monotone,
dynamic) and student interest (low, average, high) are
independent.
State whether the chi-square goodness-of-fit test or the chi-square
test for independence is appropriate.
chi-square goodness-of-fitchi-square test for
independence
State the degrees of freedom for the test.
df =
Part...

*4.) For each of the following examples, state whether the
chi-square goodness-of-fit test or the chi-square test for
independence is appropriate, and state the degrees of freedom
(df) for the test.
Part (a)
An instructor tests whether class attendance (low, average, high)
and grade point average (low, average, high) are independent.
State whether the chi-square goodness-of-fit test or the chi-square
test for independence is appropriate.
chi-square goodness-of-fitchi-square test for
independence
State the degrees of freedom for the test.
df =...

The same formula is used to calculate the chi-square statistic
in the chi-square test for goodness-of-fit and the chi-square test
of independence. Which calculation differs along the way for these
two tests?

Practice finding degrees of freedom for a Chi-square test.
Goodness of fit
categories - 1
Independence
(rows -1)( columns -1)
Homogeneity
categories -1
Variance
n-1
To look up a p-value for Chi-Square test you need to know the
degrees of freedom.
A goodness of fit test has 7 categories. What degrees of freedom
do you use?
A test for homogeneity has 9 categories. What is the degrees of
freedom, d.f.?
A test for independence has 3 rows and 9 columns....

For a chi-square goodness-of-fit test,
what is the number of degrees of freedom, if the number of
categories in the distribution is 9? ______________
what is the critical value for a 1% level of significance?
_____________

QUESTION 1
The number of degrees of freedom for the appropriate chi-square
distribution in goodness of fit test is
A
n − 1
B
(r-1)(c-1)
C
a chi-square distribution is not used
D
k − 1
QUESTION 2
A goodness of fit test and test of independence is always
conducted as a
A
upper-tail test
B
left-tail test
C
middle test
D
lower-tail test
QUESTION 3
The number of degrees of freedom for the appropriate chi-square
distribution in a test...

What is evaluated by the chi-square test for goodness of
fit?
a. If proportions of a sample distribution match those of a
population specified by the null hypothesis
b. If the frequencies found within an individual category match
a certain shape
c. Whether the means of two or more categories differ from one
another
d. Whether two variables are related to each other or
independent

The Goodness of Fit Test and Test for Independence both use the
same formula to calculate chi-square. Why? I.e., explain the logic
of the test.

in performing a chi-square goodness of fit test for a
normal distribution, a researcher wants to make sure that all of
the expected cell frequencies are at least five. the sample is
divided into 7 intervals. thw seco d through the sixth intervals
all have expected cell frequencies of at least five. the first and
the last interval have expected cell frequencies of 1.5 each. after
adjusting the number of intervals, the freedom for the chi-square
statistic is

The Chi square test is used to (select all that apply):
Test for association between two categorical variables
Compare a categorical variable across two independent
samples
Test a single categorical variable for goodness-of-fit to a
proposed distribution
None of the above

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