Final answer:
A p-value of 0.15 in a t-test suggests there's a 15% chance of observing a difference as extreme as the one calculated if the null hypothesis is true. As it is greater than the usual significance level of 0.05, there is insufficient evidence to reject the null hypothesis, indicating that the difference between the two sets of data is not statistically significant.
Step-by-step explanation:
A p-value of 0.15 gives us information about the relationship between two sets of data when comparing them using a t-test. Specifically, the p-value indicates the probability that the observed difference between the two sample means, or a difference even greater, could occur under the assumption that the null hypothesis (which typically states there is no effect or no difference) is true. In this context, a p-value of 0.15 suggests that there is a 15% chance of observing a test statistic as extreme as the one calculated, or more extreme, if the null hypothesis is accurate.
When interpreting p-values, a common threshold for significance is 0.05. If the p-value is less than 0.05, it is often considered strong evidence against the null hypothesis, leading researchers to reject it in favor of the alternative hypothesis. However, since a p-value of 0.15 is greater than 0.05, there is insufficient evidence to reject the null hypothesis at the conventional 5% level of significance. Therefore, this specific p-value would lead us to conclude that the difference observed between the two sets of data is not statistically significant and could be due to random chance within the context of the natural variability of the data.