Question

Use a LaTeX: \chi^2

χ

2

test to test the claim that in the given contingency table,
the row variable and the column variable are independent.

Tests for adverse reactions to a new drug yielded the results
given in the table. At the 0.05 significance level, test the claim
that the treatment (drug or placebo) is independent of the reaction
(whether or not headaches were experienced).

Drug Placebo

Headaches 11 7

No Headaches 73 91

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Question 22 1 pts

Find the claim for the question above

Group of answer choices

H0: Treatment and reaction are dependent.

H1: Treatment and reaction are independent.

H0: Treatment and reaction are independent.

H1: Treatment and reaction are dependent.

H0: Treatment is dependent and reaction is independent.

H1: Treatment is independent and reaction is dependent.

H0: Treatment is independent and reaction is dependent.

H1: Treatment is dependent and reaction is independent.

Answer #1

**Solution**

Null Hypothesis H_{0}: Treatment and reactions are
independent.

Alternative Hypothesis H_{1}: Treatment and reactions
are dependent.

**Option B**

Chi-square Contingency Table Test for Independence | ||||

Drug | Placebo | Total | ||

Headaches | Observed | 11 |
7 |
18 |

Expected | 8.31 | 9.69 | 18.00 | |

No Headaches | Observed | 73 |
91 |
164 |

Expected | 75.69 | 88.31 | 164.00 | |

Total | Observed | 84 | 98 | 182 |

Expected | 84.00 | 98.00 | 182.00 | |

1.798 | chi-square | |||

1 | df | |||

.1799 | p-value | |||

3.841 | Critical value |

Test statistic value (1.798) less than critical value (3.841) we fail to reject null hypothesis by the critical value approch.

So we conclude that there is not sifficient evidence to warrant rejection of the claim that treatment and reaction are independent.

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