A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 290 people over the age of 55, 77 dream in black and white, and among 291 people under the age of 25, 12 dream in black and white. Use a 0.05 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts (a) through (c) below. a. Test the claim using a hypothesis test. Consider the first sample to be the sample of people over the age of 55 and the second sample to be the sample of people under the age of 25. What are the null and alternative hypotheses for the hypothesis test? OC. Ho: P P2 H: P, "P2 OF. Ho: Pi 2P2 H: P * P2 OA. Ho: P1 =P2 H: P,

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A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 290 people over the age of 55, 77 dream in black and white, and among 291 people under the age of 25, 12 dream in black and white. With a significance level of 0.05, the claim that the proportion of people over 55 who dream in black and white is greater than for those under 25 is tested. Complete each part below:

---

**a. Test the claim using a hypothesis test.**

- Consider the first sample to be people over the age of 55 and the second sample to be people under age 25. 
- Identify the null and alternative hypotheses for the hypothesis test:

  - Options:
    - A. \(H_0: p_1 \leq p_2\), \(H_1: p_1 < p_2\)
    - B. \(H_0: p_1 = p_2\), \(H_1: p_1 \neq p_2\)
    - C. \(H_0: p_1 \neq p_2\), \(H_1: p_1 = p_2\)
    - D. \(H_0: p_1 \geq p_2\), \(H_1: p_1 < p_2\)
    - E. \(H_0: p_1 = p_2\), \(H_1: p_1 > p_2\)
    - F. \(H_0: p_1 \geq p_2\), \(H_1: p_1 \neq p_2\)

- **Identify the test statistic:**

  - \( z = \_\_\_\_\_\_\_\_\_\_\_ \) (Round to two decimal places)

- **Identify the P-value:**

  - \( P\text{-value} = \_\_\_\_\_\_\_\_\_\_\_ \) (Round to three decimal places)

- **Conclusion based on hypothesis test:**

  - The P-value is \( \_\_\_\_\_\_\_\_\_\_\_ \) the significance level of \( \alpha = 0.05 \), so \( \_\_\_\_\_\_\_\_\_ \) the null hypothesis. There is \( \_\_\_\
Transcribed Image Text:A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 290 people over the age of 55, 77 dream in black and white, and among 291 people under the age of 25, 12 dream in black and white. With a significance level of 0.05, the claim that the proportion of people over 55 who dream in black and white is greater than for those under 25 is tested. Complete each part below: --- **a. Test the claim using a hypothesis test.** - Consider the first sample to be people over the age of 55 and the second sample to be people under age 25. - Identify the null and alternative hypotheses for the hypothesis test: - Options: - A. \(H_0: p_1 \leq p_2\), \(H_1: p_1 < p_2\) - B. \(H_0: p_1 = p_2\), \(H_1: p_1 \neq p_2\) - C. \(H_0: p_1 \neq p_2\), \(H_1: p_1 = p_2\) - D. \(H_0: p_1 \geq p_2\), \(H_1: p_1 < p_2\) - E. \(H_0: p_1 = p_2\), \(H_1: p_1 > p_2\) - F. \(H_0: p_1 \geq p_2\), \(H_1: p_1 \neq p_2\) - **Identify the test statistic:** - \( z = \_\_\_\_\_\_\_\_\_\_\_ \) (Round to two decimal places) - **Identify the P-value:** - \( P\text{-value} = \_\_\_\_\_\_\_\_\_\_\_ \) (Round to three decimal places) - **Conclusion based on hypothesis test:** - The P-value is \( \_\_\_\_\_\_\_\_\_\_\_ \) the significance level of \( \alpha = 0.05 \), so \( \_\_\_\_\_\_\_\_\_ \) the null hypothesis. There is \( \_\_\_\
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