Answer:
The correct interpretation of a p-value of 0.005 is option B: "This means that the probability for observing the test statistic is 0.005 if the null is true."
When interpreting a p-value, it's important to understand that it measures the strength of evidence against the null hypothesis. Here's a step-by-step explanation of why option B is the correct interpretation:
1. The null hypothesis is a statement that assumes there is no significant difference or relationship between variables in a study.
2. In hypothesis testing, we collect data and calculate a test statistic, which is a measure that quantifies the difference or relationship between variables.
3. The p-value tells us the probability of observing a test statistic as extreme as, or more extreme than, the one we calculated, assuming that the null hypothesis is true.
4. A p-value of 0.005 means that if the null hypothesis is true, there is a 0.005 (or 0.5%) probability of observing the calculated test statistic or a more extreme one.
5. In other words, if the null hypothesis is true and there is truly no significant difference or relationship between variables, we would only expect to see a test statistic as extreme as or more extreme than the one we calculated about 0.5% of the time.
6. Since the p-value is small (less than a commonly used threshold like 0.05), it suggests that the observed data is unlikely to have occurred by chance alone if the null hypothesis is true.
Therefore, option B is the correct interpretation because it correctly describes the meaning of a p-value of 0.005 in the context of the null hypothesis and the probability of observing the test statistic.
Explanation:
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