Only on in 10 British Columbians think the Canadian military mission in Afghanistan has been 'very effective'

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Question:

Only on in 10 British Columbians think the Canadian military mission in Afghanistan has been 'very effective' so far, with a further 35 per cent thinking that the mission has been 'somewhat effective.'

A slim 53 per-cent majority of those surveyed say they support the use of Canada's troops for security and combat against the Taliban in Afghanistan.

These are the findings of an Ipsos Reid poll conducted on behalf of the Vancouver Sun newspaper. The survey was fielded Nov 2 - Nov 82006, with a random sample of 550 adult British Columbians. The survey has a margin of error of 4.2 percentage points, 19 times out of 20."

a) Cleary show how Ipsos Reid obtained the margin of error quoted in the third paragraph. Remember that pollsters use the "worst case" choice of p in their margin of error calculation.

b) Construct a 99% confidence interval for the percentage of adult British Columbians who think that the Canadian military mission in Afghanistan has been "very effective" so far. In your answer check the conditions, show the details of your CI construction and interpret your interval.

c) Suppose that you wanted to investigate student opinion regarding the effectiveness of the Canadian military mission in Afghanistan by taking a random sample of students. You want your estimate of the percentage of students rating the mission "very effective" to be within 2% at a 90% confidence level. How large a random sample would you need? In your calculation clearly indicate your thinking on your choice of values for pq.