Performing a One-Sample T-Test:
A one-sample t-test is a statistical hypothesis test used to determine if there is a significant difference between the mean of a sample and a known or hypothesized population mean. It's typically used when you have a single group of data and want to assess whether this group's mean differs significantly from a specific value. Here's a step-by-step guide on how to perform a one-sample t-test:
Step 1: Formulate Hypotheses:
- Null Hypothesis (H0): This represents the default assumption, stating that there is no significant difference between the sample mean (\(\bar{X}\)) and the population mean (\(\mu\)) or the hypothesized value. It typically looks like this: \(H0: \bar{X} = \mu_0\), where \(\mu_0\) is the hypothesized population mean.
- Alternative Hypothesis (Ha or H1): This represents the claim or hypothesis you want to test. It can be one of three types:
- Two-Tailed Test: \(Ha: \bar{X} \neq \mu_0\), indicating that you are testing whether the sample mean differs significantly from \(\mu_0\) in either direction.
- One-Tailed Test (Greater Than): \(Ha: \bar{X} > \mu_0\), indicating that you are testing whether the sample mean is significantly greater than \(\mu_0\).
- One-Tailed Test (Less Than): \(Ha: \bar{X} < \mu_0\), indicating that you are testing whether the sample mean is significantly less than \(\mu_0\).
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