TRUE or FALSE: The p-value of a hypothesis test is the probability that the null
hypothesisis true given the sample statistic obtained.
Ho: null hypothesis
Ha: alternative hypothesis
When you do a test, if you p-value is small enough than you can reject the null hypothesis which means there is not enough evidence to support the null.
If the p-value is large than you fail to reject the null
You are usually comparing your calculated p-value with a significance level that has been set for the test. Common levels are alpha = .01, .05 or .10.
If you are using an alpha of .05
and your p-value is .2 then you would not reject the null.
if you p-value is .001 then you would fail to reject the null.
FALSE. The p-value of a hypothesis test is not the probability that the null hypothesis is true given the sample statistic obtained. Instead, it is the probability of obtaining a sample statistic as extreme as, or more extreme than, the observed sample statistic, assuming that the null hypothesis is true.
To understand the p-value conceptually, you need to follow these steps:
1. Define the null hypothesis: The null hypothesis represents a statement of no effect or no difference in the population.
2. Collect and analyze the data: Gather the sample data and compute the appropriate test statistic (e.g., t-statistic, z-score).
3. Determine the alternative hypothesis: The alternative hypothesis is the opposite of the null hypothesis and represents the claim or effect we are interested in.
4. Calculate the p-value: Compute the probability of observing a test statistic as extreme as, or more extreme than, the one obtained from the data, assuming the null hypothesis is true.
5. Compare the p-value with the significance level: The significance level (often denoted as α) is predetermined, typically set to 0.05 or 0.01. If the p-value is less than or equal to the significance level, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
6. Interpret the results: If we reject the null hypothesis, we conclude that there is sufficient evidence to support the alternative hypothesis. If we fail to reject the null hypothesis, we conclude that there is not enough evidence to support the alternative hypothesis.
So, the p-value is a measure of evidence against the null hypothesis, not a measure of the probability that the null hypothesis is true given the sample statistic obtained.