I conducted an experiment where I tossed a coin $n=100$ times. I am assuming that the coin flips heads with a probability $p=0.5$. So that the coin is fair with a level of significance of $5%$, I want to find the range of the number of heads tossed.

I approached the problem by calculating the confidence interval for $k$, the number of heads tossed, using the student's t distribution.

Is this correct?

  • $\begingroup$ You give no detail, but it is in principle OK. Normal approximation is good enough here. It is best used with continuity correction. $\endgroup$ – André Nicolas Jul 30 '15 at 5:20

Just do some in-your-head approximations, no table-lookups: $95\,\%$ is about $2\sigma$, here $\sigma=\sqrt{npq}=5$, so anything between $40$ and $60$ heads will not raise your suspicion at this confidence level

  • $\begingroup$ Can you please elaborate on how you obtained a range of 40 and 60 heads? $\endgroup$ – vanHohenheim Jul 31 '15 at 21:55
  • $\begingroup$ I thought the way to estimate the range was [$\mu$-$1.98\sigma/\sqrt{n}$, $\mu$+$1.98\sigma/\sqrt{n}$]? (obtained $1.98$ from the student's t table for $\alpha/2=0.025$ and $n=100$.) However this does not give me a range of heads tossed between $40$ and $60$, but instead $49$ and $50$, which I know is wrong. $\endgroup$ – vanHohenheim Jul 31 '15 at 22:44

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