Final answer:
The sample size needed to reject the null hypothesis at the 0.05 level of significance, given a t value of 2.11 from two independent groups, is at least 11 participants per group, based on the critical t value and degrees of freedom.
Step-by-step explanation:
The subject of your question is related to conducting an independent-samples t test and determining the sample size needed to reject the null hypothesis at a given level of significance. In your scenario, the researcher is comparing the means of two independent groups at the 0.05 level of significance, and the calculated value of t is 2.11.
To establish the sample size needed to reject the null hypothesis, we must refer to the degrees of freedom (df) and the critical t value for a two-tailed test at the 0.05 significance level. Based on the information provided, which states that the critical value for a two-tailed test using the t29 distribution at the 0.05 level is 2.045, we can infer that there are >29 degrees of freedom involved because each group has participants and df = n1 + n2 - 2. Therefore, for a t value of 2.11 to be sufficient to reject the null hypothesis, each group must have at least 15 participants, considering a standard two-tailed t test with df = 30 - 2 = 28, since 2.11 > 2.045 (the critical value at df = 29).
So, with at least 15 participants per group, the researcher could reject the null hypothesis. However, since that option is not provided in the choices, we need to choose the highest number provided that is lower than 15 to ensure the t-value exceeds the critical value given the degrees of freedom. The correct answer is (c) 11 participants per group.