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
$p - value=square$
(round to three decimal places as needed)

Explanation:

Step1: Find the P - value for a right - tailed z - test

For a right - tailed z - test, the P - value is \(P(Z>z)\). Given \(z = 0.46\).
We know that \(P(Z>z)=1 - P(Z\leq z)\).
From the standard normal table, \(P(Z\leq0.46)=0.6772\).

Step2: Calculate the P - value

\(P - value=1 - 0.6772 = 0.3228\approx0.323\)

Answer:

\(0.323\)