A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 298 people over the age of 55, 69 dream in black and whit among 310 people under the age of 25, 15 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 an 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? OA. Ho: P1 P2 H₁: P₁ P₂ OD. Ho: P1 P2 H₁: P₁ P₂ Identify the test statistic (Round to two decimal places as needed.) OB. Ho: P1 SP₂ H₁: P₁ P₂ ICCEID OE Ho: P1 P2 H₁: P₁ P2 C. Ho: P1 P2 P2 H₁: P₁ OF. Ho: P1 P2 H₁: P₁ P₂

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The image contains a question regarding a hypothesis test from a study on dreaming in black and white versus color. The study involves two groups: people over the age of 55 and those under 25. Specifically, it examines the following:

### Study Background
- **Participants**: 
  - Over age 55: 298 people, of which 69 dream in black and white.
  - Under age 25: 310 people, of which 12 dream in black and white.
- **Objective**: Test the claim that the proportion of people over 55 who dream in black and white is greater than that of those under 25.
- **Significance Level**: 0.01

### Hypothesis Test
The task is to test the claim using a hypothesis test with the null and alternative hypotheses outlined below:

### Hypotheses
- **Null Hypothesis (H₀)**: \( p_1 = p_2 \)  (Proportions of people dreaming in black and white are equal for both age groups)
- **Alternative Hypothesis (H₁)**: \( p_1 > p_2 \) (A greater proportion of people over 55 dream in black and white compared to those under 25)

A correct answer is highlighted: \( H₀: p_1 = p_2 \) and \( H₁: p_1 > p_2 \).

### Task
- Identify the test statistic needed for this hypothesis test.

### Additional Features
- There is an option to "Clear all" inputs or "Check answer" on the interface.
- Functionality to view similar examples and get more help is available.

This setup is typical for evaluating differences in proportions between two independent samples using hypothesis testing.
Transcribed Image Text:The image contains a question regarding a hypothesis test from a study on dreaming in black and white versus color. The study involves two groups: people over the age of 55 and those under 25. Specifically, it examines the following: ### Study Background - **Participants**: - Over age 55: 298 people, of which 69 dream in black and white. - Under age 25: 310 people, of which 12 dream in black and white. - **Objective**: Test the claim that the proportion of people over 55 who dream in black and white is greater than that of those under 25. - **Significance Level**: 0.01 ### Hypothesis Test The task is to test the claim using a hypothesis test with the null and alternative hypotheses outlined below: ### Hypotheses - **Null Hypothesis (H₀)**: \( p_1 = p_2 \) (Proportions of people dreaming in black and white are equal for both age groups) - **Alternative Hypothesis (H₁)**: \( p_1 > p_2 \) (A greater proportion of people over 55 dream in black and white compared to those under 25) A correct answer is highlighted: \( H₀: p_1 = p_2 \) and \( H₁: p_1 > p_2 \). ### Task - Identify the test statistic needed for this hypothesis test. ### Additional Features - There is an option to "Clear all" inputs or "Check answer" on the interface. - Functionality to view similar examples and get more help is available. This setup is typical for evaluating differences in proportions between two independent samples using hypothesis testing.
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