Angus Reid Strategies regularly surveys Canadians as to whether they prefer an elected head of state instead of a monarch. The percentage preferring an elected head of state was 43% in November 2009, 30% in July 2010, and 40% in April 2013 based on surveys of 1005 Canadian adults each year.

a) Test whether support for an elected head of state in 2013 was lower than 43% at the 1% significance level, and interpret the result.

b) Suppose support among all Canadians for an elected head of state in 2013 was in fact 41%. Calculate the power of the test in part (a). Interpret the result, explaining what makes the test powerful or not powerful.

c) Test whether support for an elected head of state in 2013 was more than 5% higher than it had been in 2010 at the 5% significance level, and interpret the result.