Quiz Question: Researchers are interested in whether global temperature in 2015- 2020 has been warmer than in the decade from 2005-2014. Climate-change skeptics claim that temperatures in 2015-2020 were no warmer than in 2005-2014. Some evidence on this issue comes from two samples of monthly data for the world, one collected from January 2015 to November 2020, and the other collected over 2005-2014. The sample average temperature in 2015-2020 was 58.1 degrees with a sample standard deviation of 2 degrees. (The number of months in the 2015- 2020 sample is 71.) From the 2005-2014 period, the sample average temperature was 57.0 degrees with a sample standard deviation of 1 degree. (The number of months in the 2005-2014 sample is 120.)1. Describe carefully the assumptions you are making about the data-generating process. 2. write down and explain the null and alternative hypotheses. 3. Write down the test statistic and explain in detail how it is distributed when the null hypothesis is true. Also explain in detail how the test statistic behaves when the null hypothesis is false. 4. State the probability of Type I Error you will use in designing the test. 5. Show in a graph the test rejection region you would use. Be sure to label the distribution of the test statistic when the null hypothesis is true and indicate precisely where the probability of Type 1 Error is depicbed in your graph. 6. Calculate the test statistic. .5". Say whether you reject or do not reject the null hypothesis, and explain why