Question

A researcher conducted a goodness-of-fit test by using categorical data. Her data consists of 4 categories. Her null hypothesis states that the data occur in each category with the same frequency. If she found the test statistic χ2=χ2=12.03:

What is the degree of freedom of the χ2χ2 statistic? 3

**What is the P-value of the goodness-of-fit test? (Round
to 3 decimals)**

Answer #1

A researcher conducted a goodness-of-fit test.

Her data consists of 4 categories.

K=4

null hypothesis :- the data occur in each category with the same frequency.

Chi square statistics = = 12.03:

What is the degree of freedom :-

Df = k - 1 = 4 - 1 = 3

What is the P-value of the goodness-of-fit test

Excel command :-

CHIDIST (
, df ) = CHIDIST(12.03, 3 ) = **0.007.**

P.value = 0.007 < 0.05 =alpha

This is statistically significant

You are conducting a multinomial Goodness of Fit hypothesis test
for the claim that the 4 categories occur with the following
frequencies:
HoHo :
pA=0.1pA0.1; pB=0.5pB0.5; pC=0.3pC0.3; pD=0.1pD0.1
Complete the table. Report all answers accurate to three decimal
places.
Category
Observed
Frequency
Expected
Frequency
A
23
B
54
C
37
D
8
What is the chi-square test-statistic for this data?
χ2=
What is the P-Value?
P-Value =
For significance level alpha 0.01,
What would be the conclusion of this hypothesis test?
Reject the...

You are conducting a multinomial Goodness of Fit hypothesis test
for the claim that the 4 categories occur with the following
frequencies:
Ho: pA=0.3; pB=0.1; pC=0.4; pD=0.2
Complete the table. Report all answers accurate to three decimal
places.
Category
Observed
Frequency
Expected
Frequency
A
52
B
34
C
52
D
37
What is the chi-square test-statistic for this data? (2 decimal
places)
χ2=
What is the P-Value? (3 decimal places)
P-Value =
For significance level alpha 0.1,
What would be...

You are conducting a multinomial Goodness of Fit hypothesis test
for the claim that the 4 categories occur with the following
frequencies:
HoHo :
pA=0.4pA0.4; pB=0.25pB0.25; pC=0.25pC0.25; pD=0.1pD0.1
Complete the table. Report all answers accurate to two decimal
places, unless otherwise specified.
Category
Observed
Frequency
Expected
Frequency
A
39
B
18
C
30
D
7
What is the chi-square test-statistic for this data? (Round to two
decimal places)
χ2=χ2
What is the P-Value? (Round to four decimal places)
P-Value =

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 =

You intend to conduct a goodness-of-fit test for a multinomial
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subjects.
What are the degrees of freedom for the χ2 distribution for this
test?
df=

Test the following hypotheses by using the χ2 goodness of fit
test.
H0: pA = 0.2, pB = 0.4, and pC = 0.4
Ha: The population proportions are not pA = 0.2, pB = 0.4, and
pC = 0.4
A sample of size 200 yielded 40 in category A, 120 in category
B, and 40 in category C. Use = .01 and test to see whether the
proportions are as stated in H0.
A) Use the p-value approach.
X^2_____
a.)...

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
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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-Squared Goodness of Fit Test about a distribution that
has the following characteristics:
Category 1: 20%
Category 2: 30%
Category 3: 10%
Category 4: 15%
Category 5: 25%
complete the table and compute the test statistic.
Round to the fourth as needed.
Categories
Observed
Frequency
Expected
Frequency
1
123
2
205
3
75
4
116
5
164
Test Statistic =

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
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Which of the following statements is true in the context of a
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Select one:
a. The critical value will come from the standard normal table
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