State the null and alternative hypotheses for the statistical test described below. Testing to see if there is evidence that the correlation between two variables is negative. : 42 : P2 : 0 :: * P1 : P2 :: r Ho O vs Ho Họ: :: :: :: :: :: ::
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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**State the Null and Alternative Hypotheses for the Statistical Test Described Below:**
Testing to see if there is evidence that the correlation between two variables is negative.
[An interactive interface is displayed with selectable statistical symbols and notations. The options available include symbols for equality, inequality, less than, greater than, population mean (μ), sample mean (\(\bar{x}\)), correlation (ρ), and more.]
**Hypotheses:**
- Null Hypothesis (H₀): [Select appropriate symbols]
- Alternative Hypothesis (Hₐ): [Select appropriate symbols]
**Options to fill in the hypotheses include:**
- ≠
- <
- >
- =
- μ
- μ₁
- μ₂
- p
- p₁
- p₂
- 0
- ρ
- \(\bar{x}\)
- \(\bar{x}_1\)
- \(\bar{x}_2\)
- \(\hat{p}\)
- \(\hat{p}_1\)
- \(\hat{p}_2\)
- r
**Tools Available:**
- **eTextbook and Media** [for reference and learning]
- **Save for Later** [option to save progress]
**Submit Answer:** [Button to submit the hypothesis selection]
**Attempts:** Unlimited
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Educational Note: In hypothesis testing, the null hypothesis generally represents the status quo or a statement of no effect or no difference. The alternative hypothesis is what is tested against the null hypothesis and represents the outcome the test is designed to support. In this case, the test aims to determine if there is negative correlation evidence between two variables.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe67b822a-1066-430d-9a54-dac5dc30eee6%2F4ec51da7-d04b-4401-b6e7-0c4e6e814ed2%2F80ad86h_processed.png&w=3840&q=75)
![State the null and alternative hypotheses for the situation described below for a statistical test.
Testing to see if there is evidence that the proportion of people who smoke is greater for males than for females.
Let group 1 be the males and let group 2 be the females.
Below the text, there is an interactive equation editor with various statistical symbols and operators. The available options include:
- Equality and inequality symbols: \( = \), \( \neq \), \( < \), \( \leq \), \( > \), \( \geq \).
- Mean symbols: \( \mu \), \( \mu_1 \), \( \mu_2 \).
- Proportion symbols: \( p \), \( \hat{p} \), \( p_1 \), \( \hat{p_1} \), \( p_2 \), \( \hat{p_2} \).
- Other statistical symbols: \( - \), \( \rho \), \( \overline{x} \), \( \overline{x_1} \), \( \overline{x_2} \), \( r \).
The equation editor appears as a series of buttons representing these symbols, above a fill-in-the-blank area for entering the null hypothesis (\( H_0 \)) and the alternative hypothesis (\( H_a \)). This editor helps users formulate and select the appropriate statistical symbols to construct their hypotheses.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe67b822a-1066-430d-9a54-dac5dc30eee6%2F4ec51da7-d04b-4401-b6e7-0c4e6e814ed2%2Ftei8tsm_processed.png&w=3840&q=75)
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