Final answer:
You feel most confident about rejecting the null hypothesis at the smallest p-value of 0.01. A smaller p-value provides stronger evidence against the null hypothesis, depending on it being lower than the chosen significance level (alpha). For an alpha of 0.01, p-values less than this threshold would lead you to reject the null hypothesis.
Step-by-step explanation:
Understanding P-Values in Hypothesis Testing
When deciding whether to reject the null hypothesis in hypothesis testing, a smaller p-value indicates stronger evidence against the null hypothesis. Each option provided, a) 0.01, b) 0.05, c) 0.10, and d) 0.20, represents different p-values that could result from a statistical test. The smaller the p-value, the more confident we can be in rejecting the null hypothesis, assuming the p-value is smaller than the chosen significance level, α (alpha). In this context, we feel most confident about rejecting the null hypothesis at the smallest p-value of 0.01 (option a), because it signifies very strong evidence against the null hypothesis.
When you conduct an independent-samples t test, or any other statistical test, your decision to reject or not reject the null hypothesis is based on whether the p-value is less than the chosen alpha level. For an alpha of 0.01, you would reject the null hypothesis if the p-value is less than 0.01. Similarly, with an alpha of 0.05, a p-value less than 0.05 would lead to rejecting the null hypothesis.
For example, if you were testing whether women visit their doctor more than 5.8 times a year and obtained a p-value of 0.0165, you would reject the null hypothesis at an alpha of 0.05, concluding there is sufficient evidence for the alternative hypothesis. Conversely, a p-value of 0.0187 against an alpha of 0.01 means you would not reject the null hypothesis at this stricter significance level.