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Chapter 1: Problem 78

To examine whether planting trees reduces air pollution, we find a sample of city blocks with similar levels of air pollution and we then plant trees in half of the blocks in the sample. After waiting an appropriate amount of time, we measure air pollution levels.

Short Answer

Expert verified
The hypothesis was tested by identifying a control group and an experimental group, both with similar levels of pollution. After planting trees in the experimental group and waiting for a significant amount of time, the pollution levels of both groups were compared. A statistical test such as a t-test was used to determine whether the mean pollution levels of the groups were significantly different, allowing us to either reject or fail to reject our hypothesis.

Step by step solution

01

Identifying the groups

In this experiment, there are two groups, referred to as the 'control group' and the 'experimental group'. The control group is the half of city blocks where no trees were planted. The experimental group is the half of the city blocks where trees were planted. Both groups started with similar levels of air pollution.
02

Formulating the hypothesis

We now need to formulate our hypotheses: The null hypothesis, denoted by \(H_0\), is that planting trees has no effect on reducing air pollution levels. The alternative hypothesis, denoted by \(H_1\) or \(Ha\), is that planting trees reduces air pollution levels.
03

Collecting Data

After a significant amount of time has passed (to give the trees time to potentially affect the pollution levels), the levels of air pollution in both the control and experimental groups are measured.
04

Statistical testing

Here's where we actually test our hypothesis. We can use a variety of statistical tests for this, but a common choice would be a t-test. By comparing the means of the two groups, we can determine whether there is a statistically significant difference in pollution levels. If there is a significant difference, we can reject the null hypothesis in favor of the alternative. If there is not, we fail to reject the null hypothesis.

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