Question

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

Answer #1

**a. If proportions of a sample distribution match those
of a population specified by the null hypothesis**

Explanation:

We know that the null and alternative hypotheses for the Chi-square test for the goodness of fit are given as below:

Null hypothesis: H_{0}: Data follows the given
distribution.

Alternative hypothesis: H_{a}: Data do not follow the
given distribution.

So, we check whether proportions of a sample distribution match those of a population specified by the null hypothesis.

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...

In performing a chi-square goodness-of-fit test with multinomial
probabilities, the ___________ the difference between observed and
expected frequencies, the higher the probability of concluding that
the probabilities specified in the null hypothesis are correct.
larger
smaller

*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 =...

A
chi-square goodness of
fit test determines whether a set of observed frequencies
differs from a set of ______ frequencies.
Select one:
a. independent.
b. obtained.
c. expected.
d. constant.

You are conducting a multinomial Chi-Square Goodness of Fit
hypothesis test for the claim that the 4 categories occur with the
following frequencies:
HoHo : pA=0.1; pB=0.5; pC=0.1; pD=0.3
Complete the table. Report all answers accurate to three decimal
places.
Category
Observed
Frequency
Expected
Frequency
A
17
B
25
C
6
D
16
What is the chi-square test-statistic for this data?
χ2=
What is the P-Value?
P-Value =

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...

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?
_____________

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?

what are one of the main characteristics of chi Square
analysis Goodness-to-fit test? What type of research instrument
would be a great fit for Chi Square analysis Goodness-to-fit
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

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