When Brett Kavanaugh was nominated to be a Supreme Court justice, a survey of 1026 Americans showed that $51.5 \%$ of them disapproved of Kavanaugh. A newspaper published an article with this headline: "Majority of Americans Disapprove of Kavanaugh." Use a 0.05 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. distribution. Let $p$ denote the population proportion of all Americans who disapproved of Kavanaugh. Identify the null and alternative hypotheses. (Type integers or decimals. Do not round.) Identify the test statistic. \[ z= \] (Round to two decimal places as needed.) Identify the P-value. P-value $=$ (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. the null hypothesis. There sufficient evidence to the claim that a majority of Americans disapproved of Kavanaugh.

Step 1 ：Set up the null and alternative hypotheses. The null hypothesis (H0) is that the population proportion of Americans who disapproved of Kavanaugh is 0.5 (or 50%), which is the threshold for a majority. The alternative hypothesis (H1) is that the population proportion is greater than 0.5, which would support the claim made in the headline.

Step 2 ：Calculate the test statistic. This is done by subtracting the hypothesized population proportion (under H0) from the sample proportion, and then dividing by the standard error of the proportion. The standard error is calculated as the square root of [(p(1-p))/n], where p is the sample proportion and n is the sample size.

Step 3 ：Calculate the P-value, which is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated, under the null hypothesis. We can use the normal distribution to approximate this probability.

Step 4 ：The test statistic (z) is approximately 0.96, and the P-value is approximately 0.168.

Step 5 ：The P-value is greater than the significance level of 0.05, which means we do not reject the null hypothesis. There is not enough evidence to support the claim that a majority of Americans disapproved of Kavanaugh.

Step 6 ：Final Answer: The null hypothesis is that the population proportion of Americans who disapproved of Kavanaugh is 0.5. The alternative hypothesis is that the population proportion is greater than 0.5. The test statistic is approximately \(\boxed{0.96}\). The P-value is approximately \(\boxed{0.168}\). There is not enough evidence to reject the null hypothesis. Therefore, there is not enough evidence to support the claim that a majority of Americans disapproved of Kavanaugh.