Question

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 =

Answer #1

From the given proportions the expected frequencies are first
computed as:

Total Frequency = 17 + 25 + 6 + 16 = 64

E(A) = 0.1*64 = 6.4

E(B) = 0.5*64 = 32

E(C) = 0.1*64 = 6.4

E(D) = 0.3*64 = 19.2

The chi square test statistic here is obtained as:

**Therefore 19.6458 is the required chi square test
statistic value here.**

b) For n - 1 = 3 degrees of freedom, the p-value here is obtained from the chi square distribution tables as:

**Therefore 0.0002 is the required p-value
here.**

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 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 hypothesis test (αα = 0.05) for
the claim that all 5 categories are equally likely to be
selected.
Category
Observed
Frequency
A
14
B
19
C
11
D
8
E
21
What is the chi-square test-statistic for this data?
χ2=χ2=
What are the degrees of freedom for this test?
d.f. =
What is the p-value for this sample? (Report answer accurate to
four decimal places.)
p-value =

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

You are conducting a multinomial hypothesis test (αα = 0.05) for
the claim that all 5 categories are equally likely to be selected.
Complete the table.
Category
Observed
Frequency
Expected
Frequency
A
19
B
9
C
21
D
9
E
7
Report all answers accurate to three decimal places. But
retain unrounded numbers for future calculations.
What is the chi-square test-statistic for this data? (Report answer
accurate to three decimal places.)
χ2=χ2=
What are the degrees of freedom for this...

You are conducting a multinomial hypothesis test (αα = 0.05) for
the claim that all 5 categories are equally likely to be selected.
Complete the table.
Category
Observed
Frequency
Expected
Frequency
A
25
B
14
C
16
D
17
E
7
Report all answers accurate to three decimal places. But
retain unrounded numbers for future calculations.
What is the chi-square test-statistic for this data? (Report answer
accurate to three decimal places.)
χ2=χ2=
What are the degrees of freedom for this...

You are conducting a multinomial hypothesis test (αα = 0.05) for
the claim that all 5 categories are equally likely to be selected.
Complete the table.
Category
Observed
Frequency
Expected
Frequency
A
14
B
5
C
6
D
15
E
23
Report all answers accurate to three decimal places. But
retain unrounded numbers for future calculations.
What is the chi-square test-statistic for this data? (Report answer
accurate to three decimal places.)
χ2=χ2=
What are the degrees of freedom for this...

You are conducting a multinomial hypothesis test (αα = 0.05) for
the claim that all 5 categories are equally likely to be selected.
Complete the table.
Category
Observed
Frequency
Expected
Frequency
A
11
B
20
C
20
D
7
E
12
Report all answers accurate to three decimal places. But
retain unrounded numbers for future calculations.
What is the chi-square test-statistic for this data? (Report answer
accurate to three decimal places, and remember to use the unrounded
Pearson residuals in...

You are conducting a multinomial hypothesis test (α = 0.05) for
the claim that all 5 categories are equally likely to be selected.
Complete the table.
Category
Observed
Frequency
Expected
Frequency
A
13
B
8
C
23
D
24
E
12
Report all answers accurate to three decimal places. But
retain unrounded numbers for future calculations.
What is the chi-square test-statistic for this data? (Report answer
accurate to three decimal places, and remember to use the unrounded
Pearson residuals in...

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