Question

You are interested in testing if a coin is fair. That is, you are conducting the hypothesis test:

H0 : P(Heads) = 0.5

Ha : P(Heads) ≠ .5

If you flip the coin 1,000 times and obtain 560 heads. Calculate the P-value of this test, and decide whether or not to reject the null hypothesis at the 5% significance level.

Answer 1

The null hypothesis:

The alternate hypothesis:

where, is the population proportion.

Sample proportion:

Total number of samples:

Test statistic:

Critical value: ( as calculated from standard normal distribution table.)

Since,

Therefore,at 5% significance level we reject the Null Hypothesis.

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