a) A newspaper journalist is researching people's opinion on the decrease in isolation times for close contacts of COVID-19 positive individuals. The journalist took a random sample of 60 adults and found 42 individuals agreed with a decrease in isolation times for close contacts. Assume the conditions are satisfied and do NOT need to be checked here.

ii) Calculate an 80% confidence interval. SHOW BASIC WORKINGS.

iii) Interpret your confidence interval for the journalist.

b) A student made the following statement:

"Holding all else constant, as we decrease the confidence interval percentage, the confidence interval becomes wider."

State whether you agree or disagree with this student.

Briefly explain the reasoning behind your answer.