A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 321 people over the age of 55, 77 dream in black and white, and among 311 people under the age of 25, 13 dream in black and white. Use a 0.01 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? A. Ho: P1 H₁: P1 OD. Ho: P1 P2 P2 P2 H₁: P1 P2 Identify the test statistic. Z= (Round to two decimal places as needed.) B. Ho: P1 H₁ P₁ E. Ho: P1 H₁ P₁ P2 P2 .... P2 P2 A C. Ho: P1 P2 H₁: P₁ P2 OF. Ho: P12P2 H₁: P₁ P2 4

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**Hypothesis Testing for Dream Patterns in Different Age Groups**

A study was carried out to determine the proportion of individuals who dream in black and white versus color. The sample data includes:

- 321 people over the age of 55, out of which 77 dream in black and white.
- 311 people under the age of 25, of whom 13 dream in black and white.

The aim is to test the hypothesis at a 0.01 significance level that the proportion of people over 55 who dream in black and white is greater than that of people under 25.

**Step a: Hypothesis Test**

We will test the claim using the following hypotheses:

- **Null Hypothesis (H₀):** The proportions are equal, \( p_1 = p_2 \)
- **Alternative Hypothesis (H₁):** The proportion for those over 55 is greater, \( p_1 > p_2 \)

Select the appropriate option for these hypotheses:

- Option A: \( H₀: p_1 = p_2 \), \( H₁: p_1 > p_2 \)

**Identify the Test Statistic:**

Calculate the test statistic \( z \) and round to two decimal places as required.
Transcribed Image Text:**Hypothesis Testing for Dream Patterns in Different Age Groups** A study was carried out to determine the proportion of individuals who dream in black and white versus color. The sample data includes: - 321 people over the age of 55, out of which 77 dream in black and white. - 311 people under the age of 25, of whom 13 dream in black and white. The aim is to test the hypothesis at a 0.01 significance level that the proportion of people over 55 who dream in black and white is greater than that of people under 25. **Step a: Hypothesis Test** We will test the claim using the following hypotheses: - **Null Hypothesis (H₀):** The proportions are equal, \( p_1 = p_2 \) - **Alternative Hypothesis (H₁):** The proportion for those over 55 is greater, \( p_1 > p_2 \) Select the appropriate option for these hypotheses: - Option A: \( H₀: p_1 = p_2 \), \( H₁: p_1 > p_2 \) **Identify the Test Statistic:** Calculate the test statistic \( z \) and round to two decimal places as required.
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