## Related questions with answers

Select the best answer. An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternative hypotheses you would use to test this claim are (a)

$H_0: \hat{p} = 0.5; H_a: \hat{p} > 0.5$

(b)

$H_0: p = 0.5; H_a: p > 0.5$

(c)

$H_0: p = 0.5; H_a: p < 0.5$

(d)

$H_0: p = 0.5; H_a: p \neq 0.5$

(e)

$H_0: p > 0.5; H_a: p = 0.5$

Solutions

VerifiedWe need to test whether more than half of all adults are in favor of a ban. Thus, we need to test whether the population proportion $p$ is greater than $0.5$.

The null hypothesis states that the population proportion $p$ is equal to $0.5$. We denote this hypothesis as

$\begin{aligned} H_0:p=0.5. \end{aligned}$

The hypotheses are statements about the population parameter:

$p$: population proportion

$\mu$: population mean

$\sigma$: population standard deviation

The null hypothesis states that the population parameter is equal to the value mentioned in the claim:

$H_0:p=50\%=0.50$

The alternative hypothesis states the opposite of the null hypothesis (according to the claim):

$H_a:p>0.50$

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