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? O A. Ho: P₁ = P₂ H₁: P₁ P2 O D. Ho: P₁ = P2 H₁: P₁>P2 O B. Ho: P₁ P₂ H₁: P₁ = P2 O E. Ho: P₁ P₂ H₁: P₁ P2 OC. Ho: P₁ = P₂ H₁: P₁ P2 OF. Ho: P₁²P₂ H₁: P₁ P2

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Chapter1: Starting With Matlab
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### Study Overview

A study was conducted to compare the proportion of people who dream in black and white versus those who dream in color. Specifically, the study looked at two groups: people over the age of 55 and people under the age of 25. Among 295 individuals over 55, 64 reported dreaming in black and white. In contrast, out of 312 individuals under 25, only 13 dream in black and white. The goal is to determine if, at a 0.05 significance level, the proportion of those over 55 dreaming in black and white is greater than the proportion for those under 25.

### Hypothesis Test

The task is to test the claim using a hypothesis test, where:

- **First Sample**: People over the age of 55.
- **Second Sample**: People under the age of 25.

The question is: What are the null and alternative hypotheses for this hypothesis test?

### Hypothesis Options

Choose from the following hypotheses:

A. \( H_0: p_1 = p_2 \)  
   \( H_1: p_1 < p_2 \)

B. \( H_0: p_1 \neq p_2 \)  
   \( H_1: p_1 = p_2 \)

C. \( H_0: p_1 = p_2 \)  
   \( H_1: p_1 \neq p_2 \)

D. \( H_0: p_1 = p_2 \)  
   \( H_1: p_1 > p_2 \)

E. \( H_0: p_1 \leq p_2 \)  
   \( H_1: p_1 \neq p_2 \)

F. \( H_0: p_1 \geq p_2 \)  
   \( H_1: p_1 \neq p_2 \)

The correct hypothesis setup for this hypothesis test involves testing whether the proportion of the first sample group (those over 55) is greater than that of the second sample group (those under 25).
Transcribed Image Text:### Study Overview A study was conducted to compare the proportion of people who dream in black and white versus those who dream in color. Specifically, the study looked at two groups: people over the age of 55 and people under the age of 25. Among 295 individuals over 55, 64 reported dreaming in black and white. In contrast, out of 312 individuals under 25, only 13 dream in black and white. The goal is to determine if, at a 0.05 significance level, the proportion of those over 55 dreaming in black and white is greater than the proportion for those under 25. ### Hypothesis Test The task is to test the claim using a hypothesis test, where: - **First Sample**: People over the age of 55. - **Second Sample**: People under the age of 25. The question is: What are the null and alternative hypotheses for this hypothesis test? ### Hypothesis Options Choose from the following hypotheses: A. \( H_0: p_1 = p_2 \) \( H_1: p_1 < p_2 \) B. \( H_0: p_1 \neq p_2 \) \( H_1: p_1 = p_2 \) C. \( H_0: p_1 = p_2 \) \( H_1: p_1 \neq p_2 \) D. \( H_0: p_1 = p_2 \) \( H_1: p_1 > p_2 \) E. \( H_0: p_1 \leq p_2 \) \( H_1: p_1 \neq p_2 \) F. \( H_0: p_1 \geq p_2 \) \( H_1: p_1 \neq p_2 \) The correct hypothesis setup for this hypothesis test involves testing whether the proportion of the first sample group (those over 55) is greater than that of the second sample group (those under 25).
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