When Brett Kavanaugh was nominated to be a Supreme Court justice, a survey of 1043 Americans showed that 50.6% of them disapproved of Kavanaugh. A newspaper published an article with this headline: "Majority of Americans Disapprove of Kavanaugh." Use a 0.01 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. Ho: P H₁: p (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.

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### Hypothesis Testing on Public Opinion About Kavanaugh

When Brett Kavanaugh was nominated to become a Supreme Court justice, a survey of 1043 Americans showed that 50.6% of them disapproved of Kavanaugh. A newspaper published an article with this headline: "Majority of Americans Disapprove of Kavanaugh." We will use a 0.01 significance level to test the claim made in that headline, applying the P-value method. The normal distribution will be used as an approximation to the binomial distribution.

#### Hypothesis Formulation

**Let \( p \) denote the population proportion of all Americans who disapproved of Kavanaugh. Identify the null and alternative hypotheses:**

- **Null Hypothesis (\( H_0 \)):** 
  - \( p = 0.5 \)

- **Alternative Hypothesis (\( H_1 \)):**
  - \( p > 0.5 \)

#### Test Statistic

**Identify the test statistic:**

- **z =** 
  - \( \) (Round to two decimal places as needed.)

#### P-value Calculation

**Identify the P-value:**

- **P-value =** 
  - \( \) (Round to three decimal places as needed.)

#### Conclusion

**State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim:**

- **Conclusion:**
  - __Reject/Fail to Reject__ the null hypothesis. There is __sufficient/insufficient__ evidence to __support/refute__ the claim that a majority of Americans disapproved of Kavanaugh.
Transcribed Image Text:### Hypothesis Testing on Public Opinion About Kavanaugh When Brett Kavanaugh was nominated to become a Supreme Court justice, a survey of 1043 Americans showed that 50.6% of them disapproved of Kavanaugh. A newspaper published an article with this headline: "Majority of Americans Disapprove of Kavanaugh." We will use a 0.01 significance level to test the claim made in that headline, applying the P-value method. The normal distribution will be used as an approximation to the binomial distribution. #### Hypothesis Formulation **Let \( p \) denote the population proportion of all Americans who disapproved of Kavanaugh. Identify the null and alternative hypotheses:** - **Null Hypothesis (\( H_0 \)):** - \( p = 0.5 \) - **Alternative Hypothesis (\( H_1 \)):** - \( p > 0.5 \) #### Test Statistic **Identify the test statistic:** - **z =** - \( \) (Round to two decimal places as needed.) #### P-value Calculation **Identify the P-value:** - **P-value =** - \( \) (Round to three decimal places as needed.) #### Conclusion **State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim:** - **Conclusion:** - __Reject/Fail to Reject__ the null hypothesis. There is __sufficient/insufficient__ evidence to __support/refute__ the claim that a majority of Americans disapproved of Kavanaugh.
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