Question

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.) Repeat the test using the critical value approach.

χ^{2}_{.01}= ______ (to 3 decimals)

χ2 =_________ (to 2 decimals)

Answer #1

here applying chi square test;

relative | observed | Expected | residual | Chi square | |

category | frequency |
O_{i} |
E_{i}=total*p |
R^{2}_{i}=(O_{i}-E_{i})/√E_{i} |
R^{2}_{i}=(O_{i}-E_{i})^{2}/E_{i} |

A | 0.2 | 40 | 40.00 | 0.00 | 0.000 |

B | 0.4 | 120 | 80.00 | 4.47 | 20.000 |

C | 0.4 | 40 | 80.00 | -4.47 | 20.000 |

total | 1.000 | 200 | 200 | 40.000 |

A) Use the p-value approach

X^{2} =40.000

p value =0.0000

a)

Repeat the test using the critical value approach.

X^{2}_{0.01} =9.210

X^{2} =40.00

Test the following hypotheses by using the χ 2
goodness of fit test.
H 0:
p A = 0.2, p B = 0.4,
and p C = 0.4
Ha:
The population proportions are not
p A = 0.2 , p B = 0.4 ,
and p C = 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
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and p C = 0.4
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Category
Observed
Frequency
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A
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C
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D
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Category
Observed
Frequency
Expected
Frequency
A
39
B
18
C
30
D
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places.
Category
Observed
Frequency
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A
17
B
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Outcome
A
B
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D
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50
Ho : Pa = Pb = Pc = Pd = 1/4
H1 : At least one proportions is different from the others.
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