Margin of error

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  1. The maximum difference from p^\hat{p} to pp is EE

    \cdot E=Zα2p^(1p^)nE=Z_\frac{\alpha}{2} \sqrt{ \frac{ \hat{p} (1-\hat{p})}{n}}
    \cdot p^\hat{p}: the point estimate, a sample estimate
    \cdot pp: the population proportion (this is the data we are concerned with ultimately finding)
    \cdot nn: the sample size
  1. Finding the Margin of Error
    A sample of n=750n=750 is polled from a population. The sample has a critical value of Zα2=1.75Z_\frac{\alpha}{2}=1.75 with a point estimate of p^=0.44\hat{p}=0.44. What is the margin of error for estimating the population proportion?
    1. A ski mountain (Whistler) sees 25,000 visitors a day. The company running the ski mountain wishes to estimate the number of snowboarders who visit this mountain daily. The company surveys 100 people who are visiting the mountain and finds that 43 of them are snowboarders. If the company desires a confidence level of 0.90 in their calculations, what is their margin of error?
      1. A survey is done linking the number of concussions a season to hockey players. The NHL consists of 700700 players and we wish to have a confidence level of 0.950.95 (corresponding to a critical value of Zα2=1.96Z_\frac{\alpha}{2}=1.96). Let us assume that the point estimate will be p^=0.0125\hat{p}=0.0125 for every sample taken.
        1. What is the margin of error, if 20 players are sampled?
        2. What is the margin of error, if 100 players are sampled?
        3. What is the margin of error, if all 700 players in the NHL are polled?