Question

according to a certain government traffic safety 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 0.34. suppose a random sample of 102 traffic fatalities in a certain region with a large population results in 42 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?
next, interpret the test statistic.
the sample proportion is 1.53 standard error(s) above the proportion stated in the null hypothesis
(round to two decimal places as needed)
find the p-value.
p-value \\( =0.063 \\) (round to three decimal places as needed)
choose the correct conclusion for this hypothesis test
a. since p-value \\( >\alpha \\), reject the null hypothesis and conclude that there is sufficient evidence that the region has a higher proportion of traffic fatalities involving a positive bac than the country
b. since p-value \\( >\alpha \\), do not reject the null hypothesis and conclude that there is not sufficient evidence that the region has a higher proportion of traffic fatalities involving a positive bac than the country.
c. since p-value \\( <\alpha \\), do not reject the null hypothesis and conclude that there is not sufficient evidence that the region has a higher proportion of traffic fatalities involving a positive bac than the country.
d. since p-value \\( <\alpha \\), reject the null hypothesis and conclude that there is sufficient evidence that the region has a higher proportion of traffic fatalities involving a positive bac than the country

Explanation:

In hypothesis testing, if the \(P - value>\alpha\) (where \(\alpha = 0.05\) is the significance level), we fail to reject the null hypothesis. This means there is not enough evidence to support the alternative claim. Here, \(P - value=0.063>0.05=\alpha\).

Answer:

B. Since \(P - value>\alpha\), do not reject the null hypothesis and conclude that there is not sufficient evidence that the region has a higher proportion of traffic fatalities involving a positive BAC than the country.