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 α = 0.05 level of significance? start by determining whether the conditions for this hypothesis test are satisfied. because ( np_0(1 - p_0)=square) 10, the sample size is 5% of the population size, and the sample proportion satisfied. (round to one decimal place as needed)

Explanation:

Step1: Calculate \(np_0(1 - p_0)\)

Given \(n = 102\), \(p_0=0.34\)

$$
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$$

Since \(22.9>10\)

Step2: Consider sample - size and population - size relationship

Assume the region has a large population. A sample of size \(n = 102\) is likely to be less than \(5\%\) of the population size (because the region has a large population)

Step3: Check if the sample is a simple random sample

The problem states it is a random sample.

Answer:

Because \(np_0(1 - p_0)=22.9> 10\), the sample size is less than \(5\%\) of the population size, and the sample is a random sample, the requirements for testing the hypothesis about the population proportion are satisfied.