Pollution and altitude: in a random sample of 330 cars driven at low altitudes, 40 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed. In an independent random sample of 79 cars driven at high altitudes, 15 of them exceeded the standard. Can you conclude that the proportion of high-altitude vehicles exceeding the standard differs from the proportion of low-altitude vehicles exceeding the standard? Let \( p_{1} \) denote the proportion of low-altitude vehicles exceeding the standard and let \( p_{2} \) denote the proportion of high-altitude vehicles exceeding the standard. Use the \( a=0.05 \) level of significance and the critical value method. Part 1 of 5 State the null and alternate hypotheses. \[ \begin{array}{l} H_{0}: p_{1}=p_{2} \\ H_{1}: p_{1} \neq p_{2} \end{array} \] This hypothesis test is a \( \square \) two-tailed test.
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Did you know that the air quality in different altitudes can vary significantly? At low altitudes, pollution levels can be consistently higher due to proximity to industrial areas and population centers. In contrast, high-altitude environments may have lower pollution overall due to reduced vehicular traffic and natural dispersion of pollutants. Understanding these dynamics is crucial for environmental policies! When conducting hypothesis tests, one common mistake is neglecting to check the assumptions for the test you’re performing. For instance, ensure sample sizes are sufficiently large for normal approximation when analyzing proportions. Additionally, always verify that your samples are truly independent and randomly selected to avoid bias and ensure the results are a reliable representation of the population.
