(7) (15 points) A researcher wants to test a politician's claim that a majority of registered voters in her district support her. Let 1:) denote the proportion of registered voters in the district. The researcher selected a random sample of 100 registered voters in the district; 42 of them supported the politician. The following is the output: > prop.test{x=42,n=100,alternative=\"greater") 1-sample proportions test with continuity correction data: 42 out of 100, null probability 0.5 X-squared = 2.25, df = l, p-value = 0.9332 alternative hypothesis: true p is greater than 0.5 95 percent confidence interval: 0 . 3372363 1 . 0000000 sample estimates: P 0.42 (a) What are the hypotheses being tested? State them in terms of p. (b) What do you conclude? Why? (0) Are the assumptions behind the test satised