To formulate the null and alternative hypotheses for a population mean, follow these general structures:

• Null Hypothesis (H₀): The population mean is equal to a specified value.
  • Example: H0:μ=μ0H₀: \mu = \mu_0H0​:μ=μ0​ (where μ0\mu_0μ0​ is the hypothesized population mean).
• Alternative Hypothesis (Hₐ): The population mean is different from the specified value, depending on the type of test:
  • Two-tailed test: Ha:μ≠μ0Hₐ: \mu \neq \mu_0Ha​:μ=μ0​ (the mean is different).
  • Left-tailed test: Ha:μ<μ0Hₐ: \mu < \mu_0Ha​:μ<μ0​ (the mean is less).
  • Right-tailed test: Ha:μ>μ0Hₐ: \mu > \mu_0Ha​:μ>μ0​ (the mean is greater).

The choice of one-tailed or two-tailed depends on the research question or hypothesis being tested.