Confidence Interval

Question 1

You conducted a poll of 200 randomly selected British Columbians and asked each participant whether they supported Vancouver Whitecaps FC (yes or no). Only 45 people (22.5%) said yes. Calculate the 95% confidence interval for this estimate of breadth of support for Vancouver’s MLS team. Show your work.

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Question 2:

The confidence interval calculated in the previous question is a little large. Given a p̂ of 22.5% (0.225 as a proportion), how large would the sample have to be to produce a 95% confidence interval of exactly 10 percentage points in width (i.e., the interval 17.5% to 27.5%)? Show (some of) your work.

Question 3

In your poll of 200 randomly selected British Columbians you also asked each participant how many games they expected the Vancouver Whitecaps to win next year. The mean answer to this question in your sample was 17.8 with a standard deviation of 5.1. Calculate the 95% confidence interval for how many wins Vancouver’s MLS team will pick up next season in the opinion of BC residents. Show your work.

Question 4

Consider the confidence interval calculated in Question 1. Create a narrower confidence interval by replacing C = 95% with C = 90%. Show your work.

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