When for a particular degree of freedom, a null hypothesis could not be rejected at the .05 level of significance, then:

Correct option is C

When a null hypothesis is not rejected at the 0.05 level of significance, it means the test result was not significant at that level. Since the 0.01 level of significance is stricter than 0.05 (it requires stronger evidence to reject the null hypothesis), the null hypothesis will not be rejected at the 0.01 level if it couldn't be rejected at 0.05. The lower the p-value threshold (significance level), the harder it is to reject the null hypothesis.
Information booster:
1. Level of significance refers to the probability of rejecting a true null hypothesis (Type I error).
2. Common significance levels are 0.05, 0.01, and 0.1.
3. A smaller p-value (such as 0.01) requires stronger evidence to reject the null hypothesis.
4. Hypothesis testing involves comparing the p-value to the significance level.
5. If p > significance level, we fail to reject the null hypothesis.
6. The p-value indicates how extreme the data is under the assumption that the null hypothesis is true.
Additional Knowledge:
· 0.05 significance level: Often used as the threshold for statistical significance in social sciences.
· 0.01 significance level: A more stringent threshold, requiring stronger evidence to reject the null hypothesis.
· 0.1 significance level: A more lenient threshold, sometimes used in exploratory studies where the tolerance for Type I error is higher.
Key Points:
· If the null hypothesis is not rejected at 0.05, it will not be rejected at a stricter level like 0.01.
· A larger p-value indicates weaker evidence against the null hypothesis.
· A p-value is compared against the significance level to decide whether to reject or fail to reject the null hypothesis.