Problem 14BSC

test the given claim.

Is Seat Belt Use Independent of Cigarette Smoking?A study of seat belt users and nonusers yielded the randomly selected sample data summarized in the given table (based on data from “What Kinds of People Do Not Use Seat Belts?” by Helsing and Comstock,American Journal of Public Health,Vol. 67, No. 11). Test the claim that the amount of smoking is independent of seat belt use. A plausible theory is that people who smoke more are less concerned about their health and safety and are therefore less inclined to wear seat belts. Is this theory supported by the sample data?

Answer:

Step 1 of 2</p>

Number of cigarettes smoked per day | |||||

0 | 1-14 | 15-34 | 35 and over | Total | |

Wear seat belts | 175 | 20 | 42 | 6 | 243 |

Don’t wear seat belts | 149 | 17 | 41 | 9 | 216 |

Total | 324 | 37 | 83 | 15 | 459 |

The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

H0: The claim that the amount of smoking is independent of seat belt use

H1: The claim that the amount of smoking is not independent of seat belt use

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for independence.

Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic.

DF = (r - 1) (c - 1) = (2 - 1) (4 - 1) = 3

...Number of cigarettes smoked per day | |||||

0 | 1-14 | 15-34 | 35 and over | Total | |

Wear seat belts | 175 | 20 | 42 | 6 | 243 |

Don’t wear seat belts | 149 | 17 |