PROCEDIMIENTO PARA PRUEBAS DE HIPÓTESIS (PASO 1 DE 5 | HIPÓTESIS NULA Y ALTERNATIVA)
Hypothesis Testing: Understanding Null and Alternative Hypotheses
Steps in Hypothesis Testing
- The first step in hypothesis testing involves establishing the null hypothesis (H₀) and the alternative hypothesis (H₁). The null hypothesis is a statement that there is no effect or difference, serving as a baseline for comparison.
- The null hypothesis (H₀) is defined as a statement regarding a population parameter, formulated to test numerical evidence. It is denoted by H₀, indicating no change or difference; for example, it may state that the average monthly commission of electronic store salespeople is not different from 2000.
- A null hypothesis can only be rejected if sample data provides convincing evidence against it. Not rejecting H₀ does not prove its truth; it merely indicates insufficient evidence to reject it.
Understanding Alternative Hypothesis
- The alternative hypothesis (H₁), also known as the research hypothesis, describes what will be concluded if H₀ is rejected. It represents an assertion contrary to H₀ and requires sufficient sample evidence for acceptance.
- For instance, if the average usage time of motorcycles in Mexico is claimed to be 10 years, then H₀ states that this mean equals 10 years while H₁ posits that it differs from this value.
Practical Examples of Hypothesis Testing
- In practical scenarios like testing fuel efficiency in cars, researchers might assert that a new fuel injection system improves mileage beyond 10 kilometers per liter. Here, H₀ would claim the mean mileage remains at or below 10 km/liter while H₁ suggests it's greater than 10 km/liter.
- Another example involves testing whether milk containers hold at least 0.999 liters on average. In this case, H₀ asserts that the mean volume is greater than or equal to 0.999 liters while H₁ claims it's less than this amount.
Decision-Making Based on Sample Data
- When assessing product quality based on samples—like determining if parts meet specifications—hypotheses are framed around acceptable limits. For instance, if parts must average 2 inches in length, deviations could indicate quality issues.
- Thus, decisions about accepting or rejecting shipments depend on statistical tests comparing sample means against established hypotheses regarding their expected values.
Hypothesis Testing: Null and Alternative Hypotheses
Understanding the Null Hypothesis
- The null hypothesis (H₀) states that the population mean must be 2 inches, as specified in the problem statement. It does not indicate whether it should be less than or greater than this value.
- The null hypothesis is formally expressed as H₀: μ = 2, where μ represents the population mean.
Exploring the Alternative Hypothesis
- The alternative hypothesis (H₁) posits that the population mean is different from 2 inches, indicating a deviation from the null hypothesis.
- In contrast to H₀, which asserts equality, H₁ suggests inequality; thus, it is framed as H₁: μ ≠ 2.