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 0.37. Suppose a random sample of 104 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 equals 0.05 level of significance? a) What are the null and alternative hypotheses? b) Z statistic c) Find the p-value
Added by Patricia J.
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e., p = 0.37. The alternative hypothesis (H1) is that the proportion in the region is greater than the proportion in the country, i.e., p > 0.37. Show more…
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Example: In 2000, the National Highway Traffic Safety Administration reported that the proportion of traffic deaths attributable to alcohol was 40.9%. Out of 100 randomly selected traffic deaths this year, 32 were attributable to alcohol. Is there evidence that the true proportion of traffic deaths attributable to alcohol has decreased? Use 0.05 level. Step 1: Set up the null and alternative hypothesis Step 2: Calculate the test statistic. Step 3: Calculate the p-value (from your z-table). ALTERNATE METHOD: Critical Value Method Step 3: Find the critical value. Step 4: Make and justify a statistical decision. Step 4: Make & justify decision from rejection region. Step 5: State your conclusions in context of the problem.
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Let $p$ equal the proportion of drivers who use a seat belt in a country that does not have a mandatory seat belt law. It was claimed that $p=0.14$. An advertising campaign was conducted to increase this proportion. Two months after the campaign, $y=104$ out of a random sample of $n=590$ drivers were wearing their seat belts. Was the campaign successful? (a) Define the null and alternative hypotheses. (b) Define a critical region with an $\alpha=0.01$ significance level. (c) Determine the approximate $p$ -value and state your conclusion.
Some Elementary Statistical Inferences
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Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. The Chapter Problem involved passenger cars in Connecticut and passenger cars in New York, but here we consider passenger cars and commercial trucks. Among 2049 Connecticut passenger cars, 239 had only rear license plates. Among 334 Connecticut trucks, 45 had only rear license plates (based on samples collected by the author). A reasonable hypothesis is that passenger car owners violate license plate laws at a higher rate than owners of commercial trucks. Use a 0.05 significance level to test that hypothesis. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval.
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