Answer :
Final answer:
The hypothesis test using ANOVA will determine if the duration of the class influenced quiz performance. The ANOVA table will provide the necessary statistics to make a decision. If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that there is a significant difference in the mean quiz scores between the three groups. If the p-value is greater than or equal to the significance level, we fail to reject the null hypothesis and conclude that there is no significant difference in the mean quiz scores between the three groups.
Explanation:
To test the hypothesis that the duration of the class influenced quiz performance, we will use Analysis of Variance (ANOVA). ANOVA is a statistical test used to compare the means of three or more groups and determine if there are any significant differences.
Hypotheses:
- Null Hypothesis (H0): The duration of the class does not influence quiz performance. There is no significant difference in the mean quiz scores between the three groups.
- Alternative Hypothesis (Ha): The duration of the class influences quiz performance. There is a significant difference in the mean quiz scores between the three groups.
Criterion for rejecting the null hypothesis:
If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that there is a significant difference in the mean quiz scores between the three groups.
ANOVA Table:
Steps for hypothesis testing:
- Calculate the sum of squares (SS) for between groups (SSB) and within groups (SSE).
- Calculate the degrees of freedom (df) for between groups (k-1) and within groups (N-k).
- Calculate the mean square (MS) for between groups (MSB = SSB / (k-1)) and within groups (MSE = SSE / (N-k)).
- Calculate the F-statistic (F = MSB / MSE).
- Find the p-value associated with the F-statistic.
- Compare the p-value with the significance level (usually 0.05) to make a decision.
Decision:
If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that there is a significant difference in the mean quiz scores between the three groups. If the p-value is greater than or equal to the significance level, we fail to reject the null hypothesis and conclude that there is no significant difference in the mean quiz scores between the three groups.
Learn more about testing the effect of class schedule on student performance using anova here:
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