In September 2021 Canadian federal election, the Liberals achieved 33% of popular vote, while its arch rival the Conservatives obtained 34% of popular vote. Suppose that in a ran- dom sample of 50 Students from Carleton University in October 2021, 18 students indicated preference for the Liberals. (a) Calculate 95% confidence interval for the proportion of popular voters for the Lib- erals in Carleton University students. Check the conditions required for calculating the confidence interval. (b) What sample size would be required to estimate the the proportion of popular voters for the Liberals in Carleton University with 98% confidence and 1% margin of error? Assume that the proportion of popular voters in Canadian federal election in September 2021 is reflective for the population of the Carleton University students in October 2021. (c) Assume that you do not have any prior knowledge of the proportion of popular voters for the Liberals. Determine the sample size required in order to be 99% confi- dent that the sample proportion of popular voters for Liberals in Carleton University is within a margin of error of 1% of the population proportion.