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.
$z = \square$
(round to two decimal places as needed)

Explanation:

Step1: Calculate sample proportion

The sample proportion \(\hat{p}=0.507\), sample size \(n = 1066\), and \(p_0=0.5\), \(q_0 = 1 - p_0=0.5\)

Step2: Calculate the test - statistic

The formula for the test - statistic \(z=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0q_0}{n}}}\)
Substitute the values: \(\hat{p}=0.507\), \(p_0 = 0.5\), \(q_0=0.5\), \(n = 1066\)

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Answer:

\(z = 0.46\)