How to work out the test statistic of a coin flip?

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Given a fair coin, what’s the p value of getting at least 14/20 heads.

Am I correct in assuming

Null hypothesis — P(heads)=0.5 Alternate hypothesis — P(heads) !=0.5

How do I work out my test statistic?

I know my sample size=20, Xbar=14, population mean=10, but what is my standard deviation.

I’m trying to work out the p value given a significance level of 5%:

P(Z|P(heads)=0.5)?? How do I work out Z.

Am I correct in assuming that if Z is greater 1.96, that I can discard the null hypothesis?

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Sum the binomial:

$$P[n \geq 14] = \sum\limits_{n=14}^{20} {20 \choose n} .5^n .5^{20-n}= 0.0576591$$

By the way, the standard deviation of a binomial distribution is well known: $\sigma =\sqrt{n (1 - p) p}$ so the $z$ score is simple to compute.

But the question you asked is solved above.