Final Answer:
A smaller p-value indicates stronger evidence against the null hypothesis, favoring the alternative hypothesis. Therefore, if we decrease the significance level (α) from the conventional 0.05 to 0.10, the threshold for considering results as statistically significant becomes less stringent. Thus, the correct answer is a. The p-value would decrease.
Step-by-step explanation:
In hypothesis testing, the p-value is a measure of the evidence against a null hypothesis. A smaller p-value indicates stronger evidence against the null hypothesis, favoring the alternative hypothesis. Therefore, if we decrease the significance level (α) from the conventional 0.05 to 0.10, the threshold for considering results as statistically significant becomes less stringent. Consequently, it would be easier for a test to reject the null hypothesis, leading to a decrease in the p-value.
When the significance level is set at 0.10, the researcher is allowing for a higher probability of making a Type I error (rejecting a true null hypothesis). In this context, a Type I error corresponds to concluding that there is a significant effect or difference when there isn't one. By increasing α to 0.10, the researcher is essentially broadening the acceptance region for the null hypothesis, making it more likely to accept the alternative hypothesis and, thus, reducing the p-value associated with the test.
In summary, a decrease in the p-value occurs when the significance level is raised to 0.10 because this adjustment makes it less stringent for a result to be considered statistically significant, leading to a higher likelihood of rejecting the null hypothesis. Therefore, the correct answer is a. The p-value would decrease.