What are the key characteristics of a hypothesis test?
A random sample of 300 electronic components manufactured by a certain process are tested, and 25 are found to be defective. Let p represent the population proportion of components manufactured by this process that are defective. The process engineer claims that p < 0.05. Explain if a two-sided or one-sided hypothesis test would be appropriate.
What is meant by the phrase “statistically significant?”
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Key characteristics of a hypothesis test include:
1. Null Hypothesis (H0): This is a statement about the population that will be tested. The null hypothesis is usually a statement of no effect or no difference.
2. Alternative Hypothesis (H1 or Ha): This is a statement that contradicts the null hypothesis. It represents the outcome of the experiment that we hope to show.
3. Test Statistic: This is a numerical summary of the data that is used to make a decision about the null hypothesis. The test statistic is calculated from the sample data.
4. P-value: This is the probability of obtaining a test statistic as extreme as the one calculated, assuming the null hypothesis is true. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.
5. Decision: Based on the p-value, we either reject or fail to reject the null hypothesis.
In the given scenario, a one-sided hypothesis test would be appropriate. This is because the process engineer is making a claim about a specific direction (p < 0.05), not simply that p is different from 0.05.
The phrase “statistically significant” means that the result of a test is unlikely to have occurred by chance. In other words, there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis. The level of significance is often set at 0.05, meaning that there is a 5% chance of rejecting the null hypothesis when it is true.
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