The Kyoto Protocol was signed in 1997, and required countries to start reducing their carbon emissions. The protocol became enforceable in February 2005. In 2004, the mean CO2 emission was 4.87 metric tons per capita. Is there enough evidence to show that the mean CO2 emission is lower in 2010 than in 2004? State the type I and type II errors in this case, consequences of each error type for this situation from the perspective of the agency overseeing the protocol, and the appropriate alpha level to use. State why you picked this alpha level.

Consider H0: the mean CO2 emission in 2010 was 4.87 metric tons per capita versus H1: the mean CO2 emission in 2010 was less than 4.87 metric tons per capita.

1. State what a Type I Error would be in this context.

a. Concluding that the mean carbon dioxide emissions decreased from 4.87 when, in fact, they didn't.

b. Concluding that the mean carbon dioxide emissions decreased from 4.87 when, in fact, they did.

c. Concluding that the mean carbon dioxide emissions didn't decrease from 4.87 when, in fact, they didn't.

d. Concluding that the mean carbon dioxide emissions didn't decrease from 4.87 when, in fact, they did.

2. State what a Type II Error would be in this context.

a. Concluding that the mean carbon dioxide emissions decreased from 4.87 when, in fact, they didn't.

b. Concluding that the mean carbon dioxide emissions decreased from 4.87 when, in fact, they did.

c. Concluding that the mean carbon dioxide emissions didn't decrease from 4.87 when, in fact, they didn't.

d. Concluding that the mean carbon dioxide emissions didn't decrease from 4.87 when, in fact, they did.

3. What are the consequences of a Type I Error? Of a Type II Error?

Make sure you clearly indicate which is which. Only your final answer (the one submitted with your last attempt will be graded.

To be clear: "rejecting the null when the null is true" is not a consequence of a Type I Error, that's just its definition. Nor, is "believing the emissions went down when they really didn't." Rather, I expect a description of what might actually happen with this belief that emissions went down, and what unknown consequences might be occurring because we've made this error.

For example, if you consider the an arrested person being put to trial. If they're convicted, but are truly innocent, then, that's a Type I error (since we're innocent (null) until proven guilty here in the US). The consequences of this error are this person being sentenced to time in/paroled from prison, having their reputation tainted, their family possibly facing financial hardship etc., when none of this should have happened. Similarly, if they're set free but are truly guilty, then that's a Type II error. The consequences of this error are this person committing this crime again, perhaps causing taxpayers more money in the long run for having to make more arrests, house more inmates, and run more trials.

4. Given your answer to the previous question, what significance level, , would you choose?

Justify your answers clearly and completely. Only your final answer to this problem will be graded.Specifically, if a Type I error is more egregious, choose a 1% significance level. If a Type II error is more egregious or if they're about the same, choose 5%. Here, you should discuss why you've compared these errors in this way.