Final answer:
If the null hypothesis is not rejected at a 5% significance level, it may or may not be rejected at a 1% level depending on the exact p-value, which determines whether the evidence is strong enough to reject the hypothesis at a stricter significance level.
Therefore, the correct answer is: option a). will sometimes be may be rejected or not.
Step-by-step explanation:
The correct answer is that the null hypothesis will sometimes be rejected, however, without additional information on the exact p-value or the differences in the effect size, we cannot determine with certainty if it will also not be rejected or will always be rejected at the 1% level.
To make this decision, we must look at the p-value calculated from the test statistic.If the p-value is greater than 0.01 but less than or equal to 0.05, the null hypothesis would not be rejected at the 5% level but would be rejected at the 1% level.
If the p-value is greater than both 0.05 and 0.01, then the null hypothesis would not be rejected at either level. The converse is also true; if the p-value is less than both significance levels, the null hypothesis would be rejected at both.