a USA Today survey found that of the gun owners surveyed 275

a USA Today survey found that of the gun owners surveyed 275 favor stricter gun laws. The survey involved 500 gun owners. Test the claim that a majority (more than 50%) of gun owners favor stricter gun laws. Use a .05 significance level.

Solution

The test hypothesis:

Ho: p=0.5 (i.e. null hypothesis)

Ha: p>0.5 (i.e. alternative hypothesis)

phat=275/500 = 0.55

The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(0.55-0.5)/sqrt(0.5*0.5/500)

=2.24

It is a right-tailed test.

Given a=0.05, the critical value is Z(0.05) = 1.645 (from standard normal table)

Since Z=2.24 is larger than 1.645, we reject the null hypothesis.

So we can conclude that a majority (more than 50%) of gun owners favor stricter gun laws

Using a formula for a binomial proportion one-sample z-test with your data included, we have:
z = .55 - .50 / ?[(.50)(.50)/500] -->note: .55 is 275/500 in decimal form.