Q.1 - The Practice of Statistics for AP

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 

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) $H_0:p=0.5;H_a:p\ne 0.5$

(e) $H_0:p>0.5;H_a:p=0.5$

Step-by-Step Solution

Answer

The null and alternative hypotheses you would use to test this claim are   (b) $H_0:p=0.5;H_a:p>0.5$

Step 1: Given Information

The hypotheses are statements about the population parameter:

$p$ : population proportion.

$\mu :$ population mean.

$\sigma :$ population standard deviation.

Step 2: Explanation

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):

$H_a:p>0.50$

Therefore, the correct answer is (B).