Question

a government watchdog association claims that 70% of americans agree that the government is inefficient and wasteful. a man works for a government agency and is asked to test this claim. he finds that in a random sample of 1165 americans, 746 agreed with this view. identify null and alternative hypotheses to this problem. \\(\circ\\) \\(\text{h}_0: p \
eq 0.70\\) \\(\text{h}_\text{a}: p = 0.70\\) \\(\circ\\) \\(\text{h}_0: p \geq 0.70\\) \\(\text{h}_\text{a}: p < 0.70\\) \\(\circ\\) \\(\text{h}_0: p = 0.70\\) \\(\text{h}_\text{a}: p \
eq 0.70\\) \\(\circ\\) \\(\text{h}_0: p \leq 0.70\\) \\(\text{h}_\text{a}: p > 0.70\\)

Explanation:

Step1: Understand Hypothesis Testing Basics

In hypothesis testing, the null hypothesis ($H_0$) is a statement of no effect or the claim being tested (usually an equality), and the alternative hypothesis ($H_a$) is what we might believe instead or what we are testing for evidence against $H_0$.

Step2: Analyze the Claim

The government watchdog association claims that 70% (so $p = 0.70$) of Americans agree. The null hypothesis should represent this claim (equality), and the alternative hypothesis is a two - tailed test here (since we are just testing if the proportion is different from 0.70, as there's no indication of a one - tailed direction from the problem description). So $H_0:p = 0.70$ and $H_a:p
eq0.70$.

Answer:

$H_0:p = 0.70$, $H_a:p
eq0.70$ (corresponding to the option: $\boldsymbol{H_0:p = 0.70\ \ H_a:p
eq0.70}$)