Suppose you want have a coin that you think might not be exactly fair, that is...

Suppose you want have a coin that you think might not be exactly fair, that is the probability of a head might be slightly different from 0.5. You would like to produce a 95% confidence interval for p, the true probability of a head. You decide that you would like the margin of error for your interval to be plus or minus 0.001 (that is plus or minus 0.1%).

How many times, n, do you need to toss the coin to be sure your CI has this margin of error, or less?

Solutions

Expert Solution

The following information is provided,
Significance Level, α = 0.05, Margin of Error, E = 0.001

The provided estimate of proportion p is, p = 0.5
The critical value for significance level, α = 0.05 is 1.96.

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.5*(1 - 0.5)*(1.96/0.001)^2
n = 960400

Therefore, the sample size needed to satisfy the condition n >= 960400 and it must be an integer number, we conclude that the minimum required sample size is n = 960400
Ans : Sample size, n = 960400

orchestra answered 1 year ago

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