In recent years, climate change has been much debated in policy and academic circles in the USE. To inform this debate, a group of scientists measures the temperature in 49 regions (picked at random) of the country over the course of a year. They find an average temperature of 33 degrees Celsius. An interest group claims that the study is awed and that the real temperature was 30 degrees or lower. Assume from previous studies that a = 14-. a) '0) Construct the 90% confidence interval for the average temperature of the sample. Does the 90% CI include the temperature that the interest group considers to be the true one? (4 points) The scientists want to convince the public that their hypothesis is right and disprove the interest group's claim. They conduct a hypothesis test to assess whether they can reject the interest group's hypothesis. Set up the null and the alternative hypothesis. (4 points) Based on question (b), calculate the appropriate test statistics for the hypothesis test. (4 points) Based on question (b), calculate the pvalue. Is this a one sided or two-sided test? (4 points) Given a level of significance (1 of 0.05, do you reject the null hypothesis given in question (b)? (4 points) Using the idea of \"status quo" (or the idea of \"conservative hypothesis\"), describe in words one reason why one could set the null hypothesis as 30 degree or lower and one reason why one would set the null hypothesis as 30 degree or higher. (2 points)