Question

when brett kavanaugh was nominated to be a supreme court justice, a survey of 1066 americans showed that 50.7% of them disapproved of kavanaugh. a newspaper published an article with the headline majority of americans disapprove of kavanaugh. use a 0.10 significance level to test the claim made in that headline. use the p - value method. use the normal distribution as an approximation to the binomial distribution.
let p denote the population proportion of all americans who disapproved of kavanaugh. identify the null and alternative hypotheses.
$h_0:p$
$h_1:p$
(type integers or decimals. do not round)

Explanation:

Step1: Determine the null hypothesis

The null hypothesis \(H_0\) is a statement of equality. Since the claim is about a majority (more than 50%), the null hypothesis is \(H_0:p = 0.5\) (because we assume no majority, i.e., the proportion is 0.5)

Step2: Determine the alternative hypothesis

The alternative hypothesis \(H_1\) is the claim we are testing. The headline claims a majority, so \(H_1:p>0.5\)

Answer:

\(H_0:p = 0.5\)
\(H_1:p>0.5\)