Inquiry 11: Germany’s Sustainability Eff orts—Statistically Signifi cant Results with a Paired t-Test

Germany’s Sustainability Efforts—Statistically Significant Results with a Paired t-Test

Next Generation Science Standards (NGSS)

Materials Needed

Dimension 1: Practices—Students will practice their ability to test a hypothesis. Dimension 2: Crosscutting Patterns—Students will observe the patterns compiled from the data and analyze the relationships and the factors that influence them. Dimension 3: Core Ideas—Statistics and hypothesis testing.

Graphing calculators Internet access and links for data • US vs. Germany CO2 Emissions • US vs. Germany Electricity Production from Renewable Resources

Phenomenon

Germany is among the top 10 in sustainability efforts. What can we learn from Germany to help combat climate change?

Engage

It is important for countries and individuals to strive for sustainability in order to combat the climate change crisis. Initiatives like the EUREF Campus in Berlin are helping communities and companies partner and expand research in renewable energy and sustainability.

Explore

Featured Sources

Explain

Students are to use the carbon dioxide (CO2) emissions data provided by the World Bank to run a paired T hypothesis test and determine if there is a difference in CO2 emissions.

Students are to use the electricity production data provided by the World Bank to run a paired T hypothesis test and determine if there is a difference in production.

• EUREF-Campus Berlin—a living lab for the energy transition (4:34 minutes) • “EUREF-Science & Research.” • “Electricity Production from Renewable Sources—Germany.” • “CO2 Emissions—Germany, United States.”

Students will find the difference of means for the CO2 emissions in Germany and the United States from 1990 to current.

Students will find the difference of means for electricity production by renewable resources in Germany and the United States from 1990 to current. Students should then draw conclusions to determine if the increase in electricity production from renewable sources contributed to a reduction in CO2 emissions.

Create a Prototype To determine if the data provide convincing evidence at the α = 0.05 significance level that there is decrease in CO2 emissions produced (in metric tons per capita), on average, in Germany compared to the United States from 1990 to today, I will run a paired sample t-test.

Elaborate

Understand: Have students draw conclusions from their research. Can we determine a relationship between the production of electricity from renewable resources and CO2 emissions? Assess: Have students write a report of their statistical findings in support of their conclusions. Act: How can we use this knowledge to affect our everyday lives and make a positive change to our environment?

Evaluate

Have students either make a presentation of their findings or create a video of how this knowledge can be used to make a positive change to our environment.

Target Grade Level: 11th and 12th grade Target Course: Statistics

LESSON OVERVIEW

In this lesson students will compare Germany’s leading sustainable environment eff orts with the rest of the world. Students will be required to collect data and use a sampling distribution for simple linear regression to determine if Germany’s sustainability eff orts are statistically signifi cant compared to America’s.

TEACHER BACKGROUND INFORMATION

Germany is ranked in the top 10 in its sustainability eff orts. This rank includes its lowered CO2 emissions and its increased ability to produce electricity from renewable resources, among other factors. The United States is ranked 41. (See the Sustainable Development Report: https://dashboards.sdgindex.org/rankings.)

SUGGESTED TIME FRAME

Three to four days

CONCEPT LIST

• Paired t-test: a one-sample t-test for the means of the diff erences of paired data

• Paired data condition: The data must be paired. • Independence assumption: If the data are paired, the groups are not independent. For these methods, it’s the diff erences that must be independent of each other. • Randomization condition • Nearly normal condition: This condition can be checked with a histogram or normal probability plot of the diff erences—but not of the individual groups.

MATERIALS NEEDED

• Scoring Rubric (Scan QR Code) • Graphing calculators or statistics applet: https://www.stapplet.com • Links for data • US vs. Germany CO2 Emissions • US vs. Germany Electricity Production from Renewable Resources

Next Generation Science Standards (NGSS) / State Content Area Standards

• Dimension 1: Practices—Students will practice their ability to test a hypothesis. • Dimension 2: Crosscutting Patterns—Students will observe the patterns compiled from the data and analyze the relationships and the factors that infl uence them. • Dimension 3: Core Ideas—Statistics and Hypothesis Testing.

➤ State Content Standards—AP Statistics VAR-8, DAT-3. Carrying out a chi-square test for goodness of fit

• 3.E. Calculate a test statistic and find a p value, provided conditions for inference are met. • 4.B. Interpret statistical calculations and findings to assign meaning or assess a claim. • 4.E. Justify a claim using a decision based on significance tests

➤ Relevant Domain(s) of Disciplinary Core Ideas Physical Sciences and Applications of Science

Science and Engineering Practices

• Asking questions (for science) • Developing and using models • Planning and carrying out investigations • Analyzing and interpreting data • Using mathematics and computational thinking • Engaging in argument from evidence • Obtaining, evaluating, and communicating information • National Academies of Sciences, Engineering, and Medicine

Crosscutting Concepts

• Patterns: Students will observe the patterns compiled from the data and analyze the relationships and the factors that influence them. • Cause and effect: investigating and explaining causal relationships

PHENOMENON / MAIN PROBLEM

Germany is among the top 10 in sustainability efforts. What can we learn from them in order to help combat climate change?

Engage

It is important for countries and individuals to strive for sustainability in order to combat the climate change crisis.

Initiatives like the EUREF Campus in Berlin are helping communities and companies partner and expand research in renewable energy and sustainability.

Have students explore the EUREF Campus virtually (https://www.youtube.com/watch?v=LVWzbahKgmc 4:34 minutes) or explore their science research through their website (https://euref.de/en/welcome/).

➤ Anticipated Guiding Questions Are they making a difference? Is there statistically significant difference in the CO2 emissions and the production from renewable resources from Germany and the US?

Explore

• Students are to use the CO2 emissions data provided by The World Bank to run a paired T hypothesis test to determine if there is a difference in CO2 emissions. (https://data.worldbank.org/indicator/EN.ATM.CO2E.PC?locations=DE-US ) • Students are to use the electricity production data provided by the World Bank to run a paired T hypothesis test to determine if there is a difference in production. (https://data.worldbank.org/indicator/EG.ELC.RNWX.ZS?locations=DE-US.

RNWX.ZS?locations=DE)

➤ Featured Sources • EUREF. (n.d.) EUREF Campus Berlin—a living lab for the energy transition. https://www.youtube.com/ watch?v=LVWzbahKgmc. (4:34 minutes) • EUREF. (n.d.) EUREF-Science & Research. https://euref.de/en/welcome/. • The World Bank. (n.d.) Electricity Production from Renewable Sources – Germany. https://data.worldbank.org/ indicator/EG.ELC.RNWX.ZS?locations=DE-US.RNWX.ZS?locations=DE. • The World Bank. (n.d.) CO2 Emissions—Germany, United States. https://data.worldbank.org/indicator/EN.ATM.

CO2E.PC?locations=DE-US.

Explain

• Students are to use the CO2 emissions data provided by the World Bank to run a paired T hypothesis test to determine if there is a difference in CO2 emissions. (https://data.worldbank.org/indicator/EN.ATM.CO2E.

PC?locations=DE-US)

Students will find the difference of means for the CO2 emissions in Germany and the United States from 1990 to current.

Students will do the following: • State their hypothesis. • Correctly identify which hypothesis test will be appropriate. • Check the appropriate assumptions and conditions necessary for the appropriate hypothesis test. • Run their hypothesis test. • Draw a conclusion based off their results for their hypothesis test. • Students are to use the electricity production data provided by the World Bank to run a paired T hypothesis test to determine if there is a difference in production. (https://data.worldbank.org/indicator/EG.ELC.RNWX.ZS?locations=DE-US.

RNWX.ZS?locations=DE)

Students will find the difference of means for the electricity production by renewable resources in Germany and the United States from 1990 to current.

Students will do the following: • State their hypothesis. • Correctly identify which hypothesis test will be appropriate. • Check the appropriate assumptions and conditions necessary for the appropriate hypothesis test. • Run their hypothesis test. • Draw a conclusion based off their results for their hypothesis test. • Students should then draw conclusions to determine if the increase in electricity production from renewable sources contributed to a reduction in CO2 emissions.

➤ Create a Prototype / Investigating Solutions ➤ CO2 Emissions Hypothesis Test Report—Answer Key To determine if the data provide convincing evidence at the α = 0.05 significance level that there is decrease in CO2 emissions produced (in metric tons per capita), on average, in Germany compared to the United States from 1990 to today, I will run a paired sample t-test.

Null hypothesis: There is no difference in CO2 emissions.

Ho: μ_GERMANY-μ_(us )= 0

Alternative hypothesis: Germany produces lower CO2 emissions than the United States.

Ha: μ_GERMANY-μ_(us )> 0

➤ Assumptions and checks • Data should be paired since it represents CO2 emissions per year. • The difference in CO2 emissions in each country is independent of each other. • We do not have to check the 10% condition because we are not sampling without replacement from a finite population. • Normal/large sample: The sample size is large, and the data do not show any outliers or strong skewness.

The conditions are met, so I can use a t-model with (n − 1)= 30 − 1 =29 df

S = 1.3589

Confidence Interval

df = n − 1 = 29

So 95% confidence interval is -8.20±0.507 or (-7.69, -8.7). We are 95% confident that the average difference in CO2 emissions was between 7.69 and 8.7 metric tons per capita lower in Germany compared to the United States.

Hypothesis test

With a P value this large, we fail to reject the null hypothesis that there is no difference in the CO2 emissions between Germany and the United States.

We do have evidence to support the claim that there is a statistical difference in the lower CO2 emissions between Germany compared to the United States.

Renewable Energy Hypothesis Test Report—Answer Key

To determine if the data provide convincing evidence at the α = 0.05 significance level that there is an increase in electricity production from renewable sources, on average, in Germany compared to the United States from 1990 to today, I will run a paired sample t-test.

Null hypothesis: There is no difference in electricity production from renewable sources.

Ho: μ_GERMANY-μ_(us )= 0

Alternative hypothesis: Germany produces greater electricity production from renewable sources than the United States.

Ha: μ_GERMANY-μ_(us )> 0

➤ Assumptions and checks • Data should be paired since it represents electricity production from renewable sources per year. • The difference in electricity production from renewable sources in each country is independent of each other. • We do not have to check the 10% condition because we are not sampling without replacement from a finite population. • Normal/large sample: The sample size is large, and the data do not show any outliers or strong skewness.

The conditions are met, so I can use a t-model with (n − 1)= 26 − 1 =25 df

S = 6.4735

Confidence Interval

df = n − 1 = 25

So 95% confidence interval is 4.53±2.615 or (1.915, 7.145). We are 95% confident that the average difference in renewable energy production was between 1.915 and 7.145 percent in Germany compared to the United States.

Hypothesis Test

With a P value this large, we fail to reject the null hypothesis that there is no difference in the electricity production from renewable sources between Germany and the United States.

We do have evidence to support the claim that there is a statistical difference in the increase in electricity production from renewable sources between Germany compared to the United States.

Elaborate

Understand: Have students draw conclusions from their research. Can we determine a relationship between the production of electricity from renewable resources and CO2 emissions?

Assess: Have students write a report of their statistical findings in support of their conclusions.

Act: How can we use this knowledge to affect our everyday lives and make a positive change to our environment?

Evaluate

Have students either make a presentation of their findings or create a video of how this knowledge can be used to make a positive change to our environment.

VIRTUAL EXCHANGE

Have students do a virtual tour of EUREF Campus to see the ongoing research and engineering that will make a positive difference globally.

CAREER CONNECTION EXPLORATION

• Statistics • Engineering • Data Analysis

Maggie Scarano (TOP 3, 2022) teaches High School Math, CP Probability & Statistics, and AP Statistics at Wando High School in Mt Pleasant, South Carolina.