Questions: A researcher calculates a one-way repeated-measures ANOVA and finds F(3,13)=3.5. Based on their results, which is true? At a p level of 0.05 , they can reject the null hypothesis. At a p level of 0.01 , they can reject the null hypothesis. At a p level of 0.05 , they will fail to reject the null hypothesis. They should fail to reject the null hypothesis.

Solution Steps

The researcher calculated the F-statistic for a one-way repeated-measures ANOVA as \( F(3, 13) = 3.5 \). To determine the significance of this result, we calculated the p-value associated with this F-statistic and its degrees of freedom. The calculated p-value is:

\[ p \approx 0.0467 \]

Next, we compare the calculated p-value with the significance levels of \( \alpha = 0.05 \) and \( \alpha = 0.01 \):

1. For \( \alpha = 0.05 \):

   • Since \( p \approx 0.0467 < 0.05 \), we can reject the null hypothesis.

2. For \( \alpha = 0.01 \):

   • Since \( p \approx 0.0467 > 0.01 \), we fail to reject the null hypothesis.

Final Answer