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 this 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
$h_0: p = 0.5$
$h_1: p > 0.5$
(type integers or decimals. do not round)
identify the test statistic
$z = 0.46$
(round to two decimal places as needed.)
identify the p - value.
$p - value = 0.323$
(round to three decimal places as needed.)
state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim
\\( \square \\) the null hypothesis. there \\( \square \\) sufficient evidence to \\( \square \\) the claim that a majority of americans disapproved of kavanaugh

Explanation:

Step1: Compare P - value and significance level

Given significance level \(\alpha = 0.10\) and \(P - value=0.323\)
Since \(P - value = 0.323>0.10=\alpha\)

Step2: Make decision about null hypothesis

According to the P - value method, when \(P - value>\alpha\), we fail to reject the null hypothesis.

Step3: State conclusion about the claim

The claim is \(p > 0.5\) (a majority). Since we fail to reject \(H_0:p = 0.5\), there is not sufficient evidence to support the claim that a majority of Americans disapproved of Kavanaugh.

Answer:

Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that a majority of Americans disapproved of Kavanaugh.