Question

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 Null Hypothesis
- Fail to reject the Null Hypothesis

Answer #1

#observed frequency | chi square χ2 | |||

Category | #observed frequency | Expected | Expected % | =(Oi-Ei)2/Ei |

A | 23 | 12.2 | 0.1 | 9.560655738 |

B | 54 | 61 | 0.5 | 0.803278689 |

C | 37 | 36.6 | 0.3 | 0.004371585 |

D | 8 | 12.2 | 0.1 | 1.445901639 |

total | 122 | 122 | 1 | 11.81420765 |

Expected frequency=Expected%*total=Expected%*122

chi square χ2 =(Oi-Ei)2/Ei
=**11.814**

P_value=P(χ2(df=3)>11.812)=**0.008**

For significance level alpha 0.01,

**P-value<
0.01 hence we reject Null
hypothesis **

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 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,
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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
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E
7
Report all answers accurate to three decimal places. But
retain unrounded numbers for future calculations.
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accurate to three decimal places.)
χ2=χ2=
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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...

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
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A
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B
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C
19
D
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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...

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