Question

Pollution and altitude: in a random sample of cars driven at low altitudes, of them exceeded a standard of grams of particulate pollution per gallon of fuel consumed. in an independent random sample of cars driven at high altitudes, 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 p₁ denote the proportion of low-altitude vehicles exceeding the standard and p₂ denote the proportion of high-altitude vehicles exceeding the standard. use the α = 0.05 level of significance and the p-ᵥₐₗᵤₑ method with the TI-84 plus calculator.

Answer 1

To analyze if the proportion of high-altitude vehicles exceeding pollution standards differs from low-altitude vehicles, perform a hypothesis test for two proportions using a TI-84 calculator, comparing the p-value to the significance level α = 0.05.

Step-by-step explanation:

To determine whether the proportion of high-altitude vehicles exceeding a pollution standard differs from the proportion of low-altitude vehicles, a hypothesis test for two independent sample proportions can be performed. We will define the null hypothesis (H0) as p1 = p2, indicating no difference in the proportions, and the alternative hypothesis (Ha) as p1 ≠ p2, suggesting a difference exists.

The procedure includes calculating a test statistic using the sample data on a TI-84 calculator and comparing the p-value with the significance level α = 0.05. If the p-value is less than 0.05, the null hypothesis is rejected, implying there is a statistically significant difference between the two proportions.