One Sample T-Test of Acid Rain Data

In this activity, you will be performing a one sample t-test analysis on the pH levels of rain collected by the Environmental Protection Agency to measure the degree of acid rain. The data was collected at a rain collection station similar to the one pictured on the left in Shenandoah National Park. The Big Meadows station is part of the National Atmospheric Deposition Program's National Trends Network. The pH scale falls between 0 and 14 where values from 0 to 6.9 are acidic, and values from 7.1 to 14 are basic.  Pure water has a pH level of 7.0, which is neutral on the scale. Typically rain water is slightly acidic, usually around 5.6 on the pH scale. Acid rain is defined as having a pH level of 5.6 or lower.

Acid rain has a major effect on the environment. It damages plants in ecosystems.  It makes streams and lakes acidic, killing fish.  Acid rain can also cause property damage, ruining the paint on cars and other items and defacing buildings and statues.  Because of  these problems, it is important to document areas where acid rain occurs and identify the sources contributing to its formation.  One of the main factors contributing to acid rain is the burning of fossil fuels to produce power. This process contributes two of the major compounds that create acid rain: sulfur dioxide (SO2) and nitrogen oxides (NOx). The EPA states that 2/3 of the nation's sulfur dioxide and 1/4 of all nitrogen oxides come from electric power generation that relies on burning fossil fuels like coal. By collecting  rain data, the EPA can determine the causes of acid rain in a particular area and measure the safety of the region's environment. 

The research question is: Is the rain water collected acidic enough to be classified as "acid" rain? Because we have stated the research question in this way, we will be comparing our data to a known value based on the definition of acid rain as rain have a pH of less than 5.6, so we will run a one-sample t-test. In addition, because we are concerned with whether our rain is acidic or not, we will have a directional alternate hypothesis.

The statistical hypotheses are:

Null Hypothesis: HO: μrainfall pH = μstandard pH (5.6)

Alternate Hypothesis: HA: μrainfall pH < μstandard pH (5.6)

Open the data set in Excel. In the column to the right of the data set, list the standard to which the data set will be compared. You should copy that value down the column until you have the same number of data points for both columns. Then, because Excel doesn't have a single-sample t-test function, conduct a two sample t-test assuming unequal variances. We assume unequal variances because our known value set has a variance of zero. This test will provide the same p-value as a single sample t-test.

Since your research question leads to a directional alternate hypothesis, this is one of the rare cases in which you will use a one-tailed test. Answer the questions below in the required general format for DIGSTATS assignments, then print the single page to turn in. Remember that you should not size the printout to a single page; if the raw data will extend beyond a single page, or if there isn't space for the data anlysis output and your answers, simply copy and paste your data anlysis output and answers into a separate worksheet and print that as a single page to turn in.

1. Given an alpha value of 0.05, does your analysis indicate that there is a statistically significant difference between the data and the acid rain standard of pH 5.6? 
2. What is the t-statistic value?
3. What is the t-critical value for a one-tailed test?
4. How can you tell if there is a statistically significant difference using the t-stat and the t-critical values?
5. What is the one-tailed p-value?
6. How can you tell if there is a statistically significant difference using the p-value and the alpha value of 0.05?
7. Does the data suggest that the area where the data was collected has an acid rain problem?         


Original work on this document was done by Central Virginia Governor's School students 
Irene Tsuei, Adam Stanley, and Maury Hiller.
(Class of '03)


Copyright 2011 Central Virginia Governor's School for Science and Technology Lynchburg, VA