Question

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

Answer #1

**Smaller**

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

Explanation:

For the chi-square goodness of fit test, if the difference between observed and expected frequencies is smaller, then total sum or test statistic will be less and this will increase the probability of do not rejecting the null hypothesis of chi square test for goodness of fit. If the difference is larger, the p-value would be smaller, and this will lead to rejection of the null hypothesis.

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 =

PLEASE ANSWER ALL QUESTIONS !
1.
When performing a Chi-Square test, what is the critical value
between the accept and reject regions for a test with 5 classes and
25 observations at the 5% level of significance?
Select one:
a. 11.070
b. 2.87
c. 2.60
d. 9.488
2. True or False: A hypothesis is a statement about a population
developed for the purpose of testing.
Select one:
True
False
3. If you ACCEPT the null hypothesis while performing a
Chi-Square...

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

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 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:
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 =

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

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...

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 =...

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