Final answer:
If a t-test produces a p-value of 0.35, and assuming a significance level (α) of 0.05, the data are not statistically significant, meaning the null hypothesis is not rejected due to insufficient evidence to support the alternative hypothesis.
Step-by-step explanation:
If a t-test produces a p-value of 0.35, this means that there is a 35% probability that the observed data could have occurred under the null hypothesis. To determine whether the data are statistically significant, we compare the p-value to the significance level, typically denoted by alpha (α). If α is set at the standard 0.05 (or 5%) and the p-value is greater than α, as it is in this case (0.35 > 0.05), we conclude that the data are not statistically significant. Therefore, we do not reject the null hypothesis. In other words, the test has not provided sufficient evidence to support the alternative hypothesis.
When making statistical decisions, it's essential to compare the significance level and the p-value. If the p-value is less than or equal to the significance level (α < p-value), we reject the null hypothesis, indicating that the data are statistically significant. However, if the p-value is greater than the significance level (α > p-value), as in the case of a p-value of 0.35 when α=0.05, we do not reject the null hypothesis, which means there is insufficient evidence to suggest that the observed effect is real, rather than just due to chance.