Question

A multinomial experiment produced the following results: (You may find it useful to reference the appropriate table: chi-square table or F table) Category 1 2 3 4 5

Frequency 57 63 70 55 55

a. Choose the appropriate alternative hypothesis to test if the population proportions differ. All population proportions differ from 0.20. Not all population proportions are equal to 0.20.

b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

c. Find the p-value.

p-value < 0.01

0.01 ≤ p-value < 0.025

0.025 ≤ p-value < 0.05

0.05 ≤ p-value < 0.10

p-value ≥ 0.10

d. Can we conclude at the 1% significance level that the population proportions are not equal?

Yes, since the p-value is less than the significance level.

No, since the p-value is less than the significance level.

Yes, since the p-value is more than the significance level.

No, since the p-value is more than the significance level.

Answer #1

a)

alternative hypothesis : Not all population proportions are equal to 0.20.

b)

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

category | frequency(p) |
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} |

1 | 1/5 | 57 | 60.000 | -0.39 | 0.150 |

2 | 1/5 | 63 | 60.000 | 0.39 | 0.150 |

3 | 1/5 | 70 | 60.000 | 1.29 | 1.667 |

4 | 1/5 | 55 | 60.000 | -0.65 | 0.417 |

5 | 1/5 | 55 | 60.000 | -0.65 | 0.417 |

total | 1.000 | 300 | 300 | 2.8000 | |

test statistic X^{2} = |
2.800 |

c)

p-value ≥ 0.10

d)

No, since the p-value is more than the significance level.

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