Question
what does p mean in hypothesis and what does mu mean in hypothesis in stats
Answers
GPT-4o mini
In the context of statistics and hypothesis testing, the symbols \( p \) and \( \mu \) have specific meanings:
1. **\( p \)**:
- In hypothesis testing, \( p \) often refers to the **p-value**. The p-value is a measure that helps determine the significance of your results in relation to the null hypothesis. It indicates the probability of obtaining results at least as extreme as the observed results, assuming that the null hypothesis is true. A smaller p-value suggests that your observed data is less likely under the null hypothesis, and thus provides stronger evidence against it. Typically, if the p-value is less than a threshold (commonly 0.05), you may reject the null hypothesis.
2. **\( \mu \)**:
- The symbol \( \mu \) typically represents the **population mean** in statistics. It is used in hypothesis testing to describe the average of a population from which a sample is drawn. In null and alternative hypotheses, you might encounter statements like \( H_0: \mu = \mu_0 \) (where \( \mu_0 \) is a specified value representing the population mean under the null hypothesis) and \( H_a: \mu \neq \mu_0 \) (indicating that the population mean is different from \( \mu_0 \)).
In summary, \( p \) generally refers to p-values in hypothesis testing, while \( \mu \) represents the mean of a population.
1. **\( p \)**:
- In hypothesis testing, \( p \) often refers to the **p-value**. The p-value is a measure that helps determine the significance of your results in relation to the null hypothesis. It indicates the probability of obtaining results at least as extreme as the observed results, assuming that the null hypothesis is true. A smaller p-value suggests that your observed data is less likely under the null hypothesis, and thus provides stronger evidence against it. Typically, if the p-value is less than a threshold (commonly 0.05), you may reject the null hypothesis.
2. **\( \mu \)**:
- The symbol \( \mu \) typically represents the **population mean** in statistics. It is used in hypothesis testing to describe the average of a population from which a sample is drawn. In null and alternative hypotheses, you might encounter statements like \( H_0: \mu = \mu_0 \) (where \( \mu_0 \) is a specified value representing the population mean under the null hypothesis) and \( H_a: \mu \neq \mu_0 \) (indicating that the population mean is different from \( \mu_0 \)).
In summary, \( p \) generally refers to p-values in hypothesis testing, while \( \mu \) represents the mean of a population.