when brett kavanaugh was nominated to be a su...
when brett kavanaugh was nominated to be a supreme court justice, a survey of 1081 americans showed that 50.9% 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. h0:p = 0.5 h1:p > 0.5 (type integers or decimals. do not round.) identify the test statistic. z = (round to two decimal places as needed.)
Answer
# Explanation:
## Step1: Calculate sample proportion and other values
Given $n = 1081$, $\hat{p}=0.509$, $p_0 = 0.5$, $q_0=1 - p_0=0.5$.
## Step2: Use the formula for the test - statistic
The formula for the test - statistic $z$ in a one - sample proportion test is $z=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0q_0}{n}}}$.
Substitute the values:
\[
\begin{align*}
z&=\frac{0.509 - 0.5}{\sqrt{\frac{0.5\times0.5}{1081}}}\\
&=\frac{0.009}{\sqrt{\frac{0.25}{1081}}}\\
&=\frac{0.009}{\sqrt{0.00023127}}\\
&=\frac{0.009}{0.0152}\\
&\approx0.59
\end{align*}
\]
# Answer:
$0.59$