According to a certain government agency for a large country, the proportion of fatal traffic accidents in the country in which the driver had a positive blood alcohol concentration (BAC) is 0.36 . Suppose a random sample of 106 traffic fatalities in a certain region results in 52 that involved a positive BAC. Does the sample evidence suggest that the region has a higher proportion of traffic fatalities involving a positive BAC than the country at the $\alpha=0.05$ level of significance? Becausé $n p_{0}\left(1-p_{0}\right)=24.4>10$, the sample size is less than $5 \%$ of the population size, and the sample is given to be random, the requirements for testing the hypothesis are satisfied. (Round to one decimal place as needed.) What are the null and alternative hypotheses? $\mathrm{H}_{0}: \nabla \nabla$ versus $\mathrm{H}_{1}: \square \nabla \square \square$ (Type integers or decimals. Do not round.)
Solution
Step 1 ：According to a certain government agency for a large country, the proportion of fatal traffic accidents in the country in which the driver had a positive blood alcohol concentration (BAC) is 0.36. Suppose a random sample of 106 traffic fatalities in a certain region results in 52 that involved a positive BAC. Does the sample evidence suggest that the region has a higher proportion of traffic fatalities involving a positive BAC than the country at the $\alpha=0.05$ level of significance?
Step 2 ：Because $n p_{0}\left(1-p_{0}\right)=24.4>10$, the sample size is less than $5 \%$ of the population size, and the sample is given to be random, the requirements for testing the hypothesis are satisfied.
Step 3 ：The null and alternative hypotheses are: Null Hypothesis, $H_{0}$: $p = 0.36$ Alternative Hypothesis, $H_{1}$: $p > 0.36$
Step 4 ：The final answer is: Null Hypothesis, $H_{0}$: $p = 0.36$ Alternative Hypothesis, $H_{1}$: $p > 0.36$
