1. In a poll of 500 likely voters, 270 responded that they would vote for the candidate from the democratic party, while 230 responded that they would vote for the candidate from the republican party. Let p denote the fraction of all likely voters who preferred the democratic candidate at the time of the poll, and let p be the fraction of survey respondents who preferred the democratic candidate. (a) Use the poll results to estimate p. 0.54 [2 marks] (b) Did the poll contain statistically significant evidence that the democratic candidate was ahead of the republican candidate at the time of the poll? Carry out a suitable test at 5% significance level. [6 marks] (c) Construct a 95% confidence interval for p. (0.496, 6.584) [2 marks] (d) Construct a 99% confidence interval for p. ( 0.483, c.$97 ) [2 marks] (e) Is the interval in (d) wider than the interval in (c)? Why? [2 marks] (f) Test the hypothesis Ho : p = 0.55 vs. H1 : p / 0.55 at a 5% significance level. [4 marks] [Total: 18 marks]