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Jul 29
An alternative hypothesis is a statement that suggests there is a difference or relationship between variables in a research study. It is typically the hypothesis that the researcher is trying to support or prove through their study, as opposed to the null hypothesis which suggests there is no difference or relationship between variables. The alternative hypothesis is usually denoted by the symbol H1.
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Google Gemini AI
Jul 29
An alternative hypothesis, denoted as $H_1$, is a statistical hypothesis that is proposed as an alternative to the null hypothesis ($H_0$). It represents a specific claim or prediction about the population parameters or relationships that differ from those stated in the null hypothesis.
Purpose:
The alternative hypothesis serves two main purposes:
- To provide a direction for the study: It specifies the predicted outcome or relationship under investigation.
- To test the null hypothesis: The alternative hypothesis acts as a benchmark against which the null hypothesis is evaluated. If the results of the statistical test support the alternative hypothesis, then the null hypothesis is rejected.
Types:
There are two main types of alternative hypotheses:
- One-tailed hypothesis: Specifies a specific direction (e.g., greater than, less than) in which the population parameter is expected to deviate from the null hypothesis.
- Two-tailed hypothesis: Indicates that the population parameter is expected to deviate from the null hypothesis in either direction (i.e., greater than or less than).
Example:
Consider a null hypothesis that states: "The mean weight of apples in a certain orchard is 100 grams."
The following alternative hypotheses could be proposed:
- One-tailed (right-tailed): "$H_1$: The mean weight of apples is greater than 100 grams."
- One-tailed (left-tailed): "$H_1$: The mean weight of apples is less than 100 grams."
- Two-tailed: "$H_1$: The mean weight of apples is not equal to 100 grams."
In conclusion, the alternative hypothesis provides a specific and testable alternative to the null hypothesis, helping researchers to determine whether there is evidence to reject the null hypothesis and support a different claim about the population parameters.
Purpose:
The alternative hypothesis serves two main purposes:
- To provide a direction for the study: It specifies the predicted outcome or relationship under investigation.
- To test the null hypothesis: The alternative hypothesis acts as a benchmark against which the null hypothesis is evaluated. If the results of the statistical test support the alternative hypothesis, then the null hypothesis is rejected.
Types:
There are two main types of alternative hypotheses:
- One-tailed hypothesis: Specifies a specific direction (e.g., greater than, less than) in which the population parameter is expected to deviate from the null hypothesis.
- Two-tailed hypothesis: Indicates that the population parameter is expected to deviate from the null hypothesis in either direction (i.e., greater than or less than).
Example:
Consider a null hypothesis that states: "The mean weight of apples in a certain orchard is 100 grams."
The following alternative hypotheses could be proposed:
- One-tailed (right-tailed): "$H_1$: The mean weight of apples is greater than 100 grams."
- One-tailed (left-tailed): "$H_1$: The mean weight of apples is less than 100 grams."
- Two-tailed: "$H_1$: The mean weight of apples is not equal to 100 grams."
In conclusion, the alternative hypothesis provides a specific and testable alternative to the null hypothesis, helping researchers to determine whether there is evidence to reject the null hypothesis and support a different claim about the population parameters.
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