Questions:
- $120$ voters, $39$ identify with radical movement.
- does this provide sufficient evidence that more than $25\%$ of voters identify with radical movement?
- use $p$-value approach.
My Steps:
(0) Check Requirements $(120)(.25)>10$ and $(120)(.75)>10$ -- passes requirements.
(1) Hypothesis will be using a right tailed test. $H_0 : p = .25; H_1 : p > .25$
(2) No alpha (level of significance) is given, so default to $0.05$.
(3) $Z_t (\text{Test Statistic}) = ((.325-.25)/(\sqrt{(.25)(.75)/120} = 1.897$
(4) $P(Z \ge 1.897) \ge 1 - (\text{about}).9713 = .0287$. Reject $H_o$ if $p$-value is less than alpha.
(5) At the $.05$ level of significance, there is sufficient evidence to support that more than $25\%$ of voters identify with the radical movement.
Does that all look correct? Thank you :-)