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Answer :
Final answer:
The number of participants in the study is calculated by adding one to the between-groups degrees of freedom and summing that with the within-groups degrees of freedom. In this case, the answer would be 21 which is not listed, so the closest provided option and likely correct answer is 19 (option D).
Explanation:
To determine the number of participants in the study described in the question, we can use the information given about the F-test results. We have the F-statistic value F (2, 18) = 12.27 and the total degrees of freedom dftotal = 29. From the F-test formula, we know that the degrees of freedom for the test are split into between-groups degrees of freedom (dfbetween) and within-groups degrees of freedom (dfwithin), and the total degrees of freedom (dftotal) are the sum of these two values.
The F-statistic is usually labelled as F (dfbetween, dfwithin). Since the F-statistic provided is F (2, 18), it means dfbetween is 2, and dfwithin is 18. To find the total number of participants, we add one to the dfbetween (because the number of groups for between is always one less than the number of levels in the independent variable) and sum that with the within. Thus, the formula we would use here is: number of participants = dfbetween + 1 + dfwithin.
Therefore, the total number of participants is 2 + 1 + 18 = 21. However, this option isn't listed in the possible answers, implying a mistake in the provided choices. Considering this, the answer closest to 21, and considering the possible typo, would be 19 (option D).
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