Question

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

$\text{а.}\mathrm{H}0:{\mathrm{p}}^{\wedge =0.5};\mathrm{Ha}:{\mathrm{p}}^{\wedge >0.5}{H}_0:\hat{p}=0.5;H_a:\hat{p}>0.5\text{.}$

$\text{b. H0:}\mathrm{p}=0.5;\text{Ha:}\mathrm{p}>0.5H_0:p=0.5;H_a:p>0.5\text{.}$

$\text{c. H0:}\mathrm{p}=0.5;\text{Ha:}\mathrm{p}<0.5H_0:p=0.5;H_a:p<0.5\text{.}$

$\text{d. H0:}\mathrm{p}=0.5;\text{Ha:}\mathrm{p}\ne 0.{\mathrm{H}}_0:p=0.5;H_a:p\ne 0.5\text{.}$

$\text{e. H0:}\mathrm{p}>0.5;\text{Ha:}\mathrm{p}=0.5H_0:p>0.5;H_a:p=0.5\text{.}$

Short answer

$\text{So, the correct answer is option (b) that is}{H}_0:p=0.5,H_a:p>0.5\text{.}$

Step-by-step solution

Step 1:Given information

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

Step 2:Explaination

The hypotheses are statements about the population parameter:

$p\text{: Population parameter.}$

$\mu :\text{Population mean.}$

$\sigma \text{: Population standard deviation.}$

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):

$H_a:p>0.50$