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?
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.