Question

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 0.38. Suppose a random sample of 112 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 a= 0.05 level of significance? Because npo (1-P) - 710, the sample size is 5% of the population size, and the sample the requirements for testing the hypothesis satisfied. (Round to one decimal place as needed.) What are the null and alternative hypotheses? (Type integers or decimals. Do not round.) Find the test statistic, 20. Zo = (Round to two decimal places as needed.) Find the P-value. P-value = (Round to three decimal places as needed.) Determine the conclusion for this hypothesis test. Choose the correct answer below. O A. Since P-value a, 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. O C. Since P-value > a, 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. OD. Since P-value

Answer 1

A hypothesis test is conducted to compare the proportion of fatal traffic accidents with positive BAC in a specific region to the overall country rate. The null and alternative hypotheses are based on whether the region's rate exceeds the country's known proportion. The test statistic and p-value are compared to the significance level to draw a conclusion.

Step-by-step explanation:

The student is asked to perform a hypothesis test for a proportion to determine if a certain region has a higher rate of traffic fatalities involving a positive blood alcohol concentration (BAC) compared to the overall country rate. The null hypothesis (H_0) would be that the region's proportion is equal to 0.38, the country's proportion, so H0: p = 0.38. The alternative hypothesis (Ha) would suggest that the region's proportion is greater, so Ha: p > 0.38.

The sample evidence yields 52 fatalities with positive BAC out of 112, giving a sample proportion of p' = 0.4643. Using the standardized test statistic for a sample proportion, Z, and the provided p-value, we compare the p-value to the significance level, α = 0.05, to decide whether to reject H_0. If the p-value is less than α, we would reject the null hypothesis and conclude that the region has a higher proportion of traffic fatalities involving a positive BAC.

Answer 2

The student's question is about performing a one-tailed hypothesis test for a population proportion based on sample evidence. The objective is to determine if the sample provides sufficient evidence to conclude if the regional proportion of traffic fatalities with a positive BAC is higher than the country's proportion. The decision will be based on comparing the calculated p-value against the significance level (α = 0.05).

Step-by-step explanation:

The question involves testing a hypothesis about a population proportion based on sample evidence. To test the hypothesis that the region has a higher proportion of traffic fatalities involving a positive BAC than the country, we use a one-tailed test.

The null hypothesis (H0) is that the proportion of traffic fatalities with a positive BAC in the region is equal to the country's proportion (p0 = 0.38). The alternative hypothesis (Ha) is that the region's proportion is higher (p > 0.38).

To calculate the test statistic (z0), we use the formula:

z0 = (p' - p0) / sqrt((p0 * (1 - p0)) / n)

Where p' is the sample proportion (52/112), p0 is the population proportion (0.38), and n is the sample size (112).

The p-value for this test statistic indicates how likely it is to observe a sample statistic as extreme as the test statistic under the null hypothesis. If the p-value is less than the significance level (α = 0.05), we reject the null hypothesis.

Based on this information, if the calculated p-value is less than 0.05, we would reject the null hypothesis and conclude that there is sufficient evidence to suggest the region has a higher proportion of traffic fatalities involving a positive BAC than the country. Otherwise, we do not reject the null hypothesis.