MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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.
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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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