Evans Okuku
Jun 9
Differentiate between the following as used in hypothesis: 1. One tailed and two tailed test ? 2. a statistic and parameter?
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ChatGPT
Jun 9
1. One tailed and two tailed test:
- One tailed test: In a one-tailed test, the hypothesis is directional and predicts the outcome in only one direction. For example, testing whether a new drug will improve test scores, with the hypothesis being that the drug will increase scores. The critical region for the test is on one side of the distribution.
- Two tailed test: In a two-tailed test, the hypothesis is non-directional and predicts the outcome in either direction. For example, testing whether a new drug will have an effect on test scores, without specifying whether the effect will be an increase or decrease. The critical region for the test is split between both sides of the distribution.
2. A statistic and parameter:
- Statistic: A statistic is a numerical value calculated from a sample of data. It is used to estimate or infer information about a population parameter. Examples of statistics include the mean, median, standard deviation, and correlation coefficient.
- Parameter: A parameter is a numerical value that describes a characteristic of a population. It is typically unknown and is what researchers aim to estimate using sample data. Examples of parameters include the population mean, population standard deviation, and population proportion.
- One tailed test: In a one-tailed test, the hypothesis is directional and predicts the outcome in only one direction. For example, testing whether a new drug will improve test scores, with the hypothesis being that the drug will increase scores. The critical region for the test is on one side of the distribution.
- Two tailed test: In a two-tailed test, the hypothesis is non-directional and predicts the outcome in either direction. For example, testing whether a new drug will have an effect on test scores, without specifying whether the effect will be an increase or decrease. The critical region for the test is split between both sides of the distribution.
2. A statistic and parameter:
- Statistic: A statistic is a numerical value calculated from a sample of data. It is used to estimate or infer information about a population parameter. Examples of statistics include the mean, median, standard deviation, and correlation coefficient.
- Parameter: A parameter is a numerical value that describes a characteristic of a population. It is typically unknown and is what researchers aim to estimate using sample data. Examples of parameters include the population mean, population standard deviation, and population proportion.
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Google Gemini AI
Jun 9
1. One-tailed and Two-tailed Tests
- One-tailed test: Assumes that the alternative hypothesis specifies the direction of the effect (e.g., greater than or less than).
- Two-tailed test: Assumes that the alternative hypothesis does not specify a direction of the effect (e.g., either greater than or less than).
2. Statistic and Parameter
- Statistic: A numerical value calculated from a sample that estimates a population parameter.
- Parameter: A numerical characteristic of a population.
Key Differences:
- Source: A statistic is calculated from a sample, while a parameter describes the entire population.
- Uncertainty: A statistic is uncertain because it is based on a sample, whereas a parameter is a fixed value for the population.
- Variability: A statistic can vary from sample to sample, while a parameter is typically fixed.
- Symbolism: Statistics are usually denoted by lowercase letters (e.g., x̄), while parameters are denoted by uppercase letters (e.g., μ).
Example:
- Statistic: Sample mean (x̄)
- Parameter: Population mean (μ)
The sample mean (x̄) is a statistic calculated from a sample and estimates the population mean (μ). The population mean is a parameter that describes the entire population.
- One-tailed test: Assumes that the alternative hypothesis specifies the direction of the effect (e.g., greater than or less than).
- Two-tailed test: Assumes that the alternative hypothesis does not specify a direction of the effect (e.g., either greater than or less than).
2. Statistic and Parameter
- Statistic: A numerical value calculated from a sample that estimates a population parameter.
- Parameter: A numerical characteristic of a population.
Key Differences:
- Source: A statistic is calculated from a sample, while a parameter describes the entire population.
- Uncertainty: A statistic is uncertain because it is based on a sample, whereas a parameter is a fixed value for the population.
- Variability: A statistic can vary from sample to sample, while a parameter is typically fixed.
- Symbolism: Statistics are usually denoted by lowercase letters (e.g., x̄), while parameters are denoted by uppercase letters (e.g., μ).
Example:
- Statistic: Sample mean (x̄)
- Parameter: Population mean (μ)
The sample mean (x̄) is a statistic calculated from a sample and estimates the population mean (μ). The population mean is a parameter that describes the entire population.
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