1) In a random survey of adults in a large metropolitan area found that 253 out of 1005 young adults (between the ages of 18 and 35) and 274 out of 1236 older adults (over the age of 35) got at least some of their news each week from National Public Radio.) a) Use the 2-PropZInt command in ti calculator to find a 95% confidence interval for the difference in the proportion of young adults and older adults who get some of their news from NPR. b) Does the interval provide evidence that there is a difference? Explain. 2) Before the 2020 Democratic National Convention, a random national sample of 697 adults, showed the favorability rating for Democratic vice-presidential nominee, Kamala Harris, to be 35%. After the convention, a random national sample of 714 adults, conducted by the same organization, showed that her favorability rating increased to 41%. The average convention bounce has been on the wane in recent years. Did Kamala Harris buck this trend? Did her favorability rating show a statistically significant improvement? Use a significance level of ?? = 0.05. a) Write the hypotheses. b) Use the 2-PropZTest command in ti calculator to run this hypothesis test. Write the command and the values entered and then report the test statistic and p-value. c) Write a conclusion for this test in the context of the problem.

3) Below are random samples of enrollments for medical schools that specialize In research and for those that specialize In primary care. Is there a difference In the average enrollment for the two specializations? Use a significance level of a = 0.05. (8 pts) Research 474 577 605 783 467 670 414 813 443 565 696 277 419 884 663 692 694 Primary Care 683 605 427 728 546 574 471 407 442 587 593 377 662 555 527 420 a) Write the hypotheses. b) Use the 2-SampTTest command in your calculator to run this hypothesis test. Write the command and the values you entered and then report the test statistic and p-value c) Write a full conclusion for this test in the context of the problem d) What type of error (Type 1 or Type 2) could exist with your conclusion? 4) Environmentalists have been testing new scrubbers that might help reduce the amount of contaminants released into the air. To see if the scrubbers were effective, daily measurements of pollutants released were taken at 10 locations before and after the scrubbers were installed. Use a significance level of a = 0.05. (10 pts) Location 1 2 3 4 5 16 8 9 10 Before Scrubbers 25 26 20 19 20 23 22 After Scrubbers 19 19 15 14 18 a) Write the hypotheses. 6) Use the T-Test command in your calculator to run this hypothesis test. Write the command and the values you entered and then report the test statistic and p-value. c) Write a full conclusion for this test in the context of the problem. d) Use the Tinterval command in your calculator to find a 90% confidence interval for the difference in the average amount of contaminants released into the air e) Does your interval show a difference in the amount of contaminants released into the air? Explain