The statement a) When the test p-value is very small, the data provide strong evidence in support of the alternative hypothesis is correct .
When the conditions for inference are met, the correct statement is:
a) When the test p-value is very small, the data provide strong evidence in support of the alternative hypothesis.
In statistical hypothesis testing, the p-value is a measure of the evidence against a null hypothesis.
The null hypothesis typically represents a default or no-effect assumption, while the alternative hypothesis represents what the researcher aims to show.
A small p-value suggests that the observed data is unlikely under the assumption of the null hypothesis, providing support for rejecting the null hypothesis in favor of the alternative.
A common significance level, often set at 0.05, is used to determine whether the evidence against the null hypothesis is strong enough.
If the p-value is less than the chosen significance level, the null hypothesis is rejected, and the alternative hypothesis is supported.
Therefore, a small p-value indicates that the data provide strong evidence against the null hypothesis, supporting the alternative hypothesis.
It's important to note that the interpretation of p-values should be done in conjunction with other considerations, such as effect size and study design, to draw meaningful conclusions from statistical analyses.