For a random sample of households in the US, we record annual household income, whether the location is east or west of the Mississippi River, and number of children. We are interested in determining whether or not there is a linear relationship between household income and number of children. Part 1 (a) State the null and alternative hypotheses. :: # Ho: CII μ vs Ha! 2 ₂ :: p :: P₁ :: P2 P₁ :: P₂ JID 0 p x 1

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For a random sample of households in the US, we record annual household income, whether the location is east or west of the Mississippi River, and number of children. We are interested in determining whether or not there is a linear relationship between household income and number of children.

**Part 1**

(a) State the null and alternative hypotheses.

Below is a set of symbols and variables that can be used to construct the hypotheses:

- \( = \)
- \( \neq \)
- \( < \)
- \( > \)
- \( \mu \)
- \( \mu_1 \)
- \( \mu_2 \)
- \( p \)
- \( p_1 \)
- \( p_2 \)
- 0
- \( \rho \)
- \( \bar{x} \)
- \( \bar{x}_1 \)
- \( \bar{x}_2 \)
- \( \hat{p} \)
- \( \hat{p}_1 \)
- \( \hat{p}_2 \)
- \( r \)

**Hypotheses Setup:**

- **Null Hypothesis (H₀):** State the hypothesis with the chosen symbols.
- **Alternative Hypothesis (H₁):** State the opposing hypothesis using the appropriate variables.
Transcribed Image Text:For a random sample of households in the US, we record annual household income, whether the location is east or west of the Mississippi River, and number of children. We are interested in determining whether or not there is a linear relationship between household income and number of children. **Part 1** (a) State the null and alternative hypotheses. Below is a set of symbols and variables that can be used to construct the hypotheses: - \( = \) - \( \neq \) - \( < \) - \( > \) - \( \mu \) - \( \mu_1 \) - \( \mu_2 \) - \( p \) - \( p_1 \) - \( p_2 \) - 0 - \( \rho \) - \( \bar{x} \) - \( \bar{x}_1 \) - \( \bar{x}_2 \) - \( \hat{p} \) - \( \hat{p}_1 \) - \( \hat{p}_2 \) - \( r \) **Hypotheses Setup:** - **Null Hypothesis (H₀):** State the hypothesis with the chosen symbols. - **Alternative Hypothesis (H₁):** State the opposing hypothesis using the appropriate variables.
**Question (b):** Which sample correlation shows more evidence of a relationship, \( r = 0.25 \) or \( r = 0.55 \)?

- ○ \( r = 0.25 \)
- ○ \( r = 0.55 \)
- ○ Both the same

There are no graphs or diagrams accompanying the text.
Transcribed Image Text:**Question (b):** Which sample correlation shows more evidence of a relationship, \( r = 0.25 \) or \( r = 0.55 \)? - ○ \( r = 0.25 \) - ○ \( r = 0.55 \) - ○ Both the same There are no graphs or diagrams accompanying the text.
Expert Solution
Step 1

Explanation:

Null hypothesis: Hρ = 0                (There is no relationship)

Alternative hypothesis: H: ρ  0        (There is a relationship)

ρ denote the population correlation coefficient.

 

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