1. **Stating the problem:** We want to develop hypotheses for situations where the null hypothesis ($H_0$) can be assumed, based on experiences measured by averages or proportions. 2. **Claim or assumption of null hypothesis:** The null hypothesis ($H_0$) usually states that there is no effect or no difference. For example, $H_0: \mu = \mu_0$ (the population mean equals a specific value) or $H_0: p = p_0$ (the population proportion equals a specific value). 3. **Alternative hypothesis ($H_a$):** This is what we want to test against $H_0$. It can be $H_a: \mu \neq \mu_0$, $H_a: \mu > \mu_0$, $H_a: \mu < \mu_0$ for means, or similarly for proportions. 4. **Method of collecting a sample:** Since the sample size should be less than 30, we use a small sample from the population. This can be done by random sampling, ensuring each member of the population has an equal chance of selection. 5. **Level of significance:** We use $\alpha = 0.05$ (5%) to decide whether to reject $H_0$. This means we accept a 5% chance of wrongly rejecting $H_0$. 6. **Testing the hypothesis:** For means, if the population standard deviation is unknown and sample size is less than 30, use the $t$-test: $$ t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}} $$ where $\bar{x}$ is the sample mean, $s$ is the sample standard deviation, and $n$ is the sample size. For proportions, use the $z$-test: $$ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} $$ where $\hat{p}$ is the sample proportion. 7. **Decision rule:** Compare the test statistic to critical values from $t$ or $z$ distribution at $\alpha=0.05$. If the test statistic falls in the rejection region, reject $H_0$; otherwise, do not reject $H_0$. This procedure allows testing claims about population averages or proportions with small samples and a 5% significance level.