I estimate that the probability of heads when tossing a coin to be $\hat{p}=\frac{6}{10}$. Which test will I use to test whether the coin is a fair coin? A) $H_{o}: \hat{p}.5, ; H_{1}: \hat{p} \ngtr .5$. B) $H_{o}: \hat{p}

Question

I estimate that the probability of heads when tossing a coin to be $\hat{p}=\frac{6}{10}$. Which test will I use to test whether the coin is a fair coin?
A) $H_{o}: \hat{p}>.5, ; H_{1}: \hat{p} \ngtr .5$.
B) $H_{o}: \hat{p}<.5, ; H_{1}: \hat{p} \nless .5$.
C) $H_{o}: \hat{p}=.5 ; H_{1}: \hat{p} \neq .5$.
D) $H_{o}: \hat{p} \geq .5, ; H_{1}: \hat{p} \geq .5$.

Quizplus · Accepted Answer

To test whether a coin is fair, you would use a two-tailed test where the null hypothesis is that the probability of heads ($\hat{p}$) is equal to 0.5, and the alternative hypothesis is that $\hat{p}$ is not equal to 0.5. This allows for the possibility that the coin could be biased towards either heads or tails.

I Estimate That the Probability of Heads When Tossing a Coin