A professor has a class with four recitation groups, each with 16 students. Determine whether or not the section choice (different TAs and different days of the week) has any relationship with how students performed on the test.

Scores for Each Group:

- Group 1: 77.2, 69.9, 62.2, 76.5, 69.8, 61.9, 51.2, 65.8, 76.2, 71.4, 49.5, 53.5, 58.7, 71.6, 73.9, 67.2
- Group 2: 68.7, 93.2, 71, 65.5, 81.8, 69.8, 70.4, 67, 74.7, 77.6, 62.7, 69.9, 64.8, 74.7, 78.9, 69.9
- Group 3: 76.8, 62.9, 81.9, 63.1, 82.1, 74, 82.9, 74.3, 63.4, 71.8, 62.7, 69.6, 71.7, 70.5
- Group 4: 69.7, 75.1, 58, 65.4, 56.7, 68.1, 66.9, 60.3, 76.3, 68.9, 89.9, 89, 69, 58.7

First, run an ANOVA with this data and fill in the summary table. (Report p-values accurate to 4 decimal places and all other values accurate to 3 decimal places.)

ANOVA Summary Table:

| Source | SS | df | MS | F-ratio | p-value |
|------------|----------|----|---------|---------|---------|
| Between | 917.233 | 3 | 305.744 | 4.249 | 0.0087 |
| Within | 4317.276 | 60 | 71.955 | | |

To follow up, the professor decides to use the Tukey-Kramer method to test all possible pairwise contrasts. What is the q critical value for the Tukey-Kramer critical range (alpha = ...)?

Based on the results of the ANOVA test, there is evidence of a relationship between the section choice and student performance on the test, as the p-value is less than the usual significance level of 0.05.

The between-group variability is statistically significant, with an F-ratio of 4.249 and p-value of 0.0087, while the within-group variability is not significant. This suggests that the differences in test scores are more likely due to the different section choices rather than random variability within groups.

To conduct pairwise comparisons, the professor can use the Tukey-Kramer method. The q critical value for the Tukey-Kramer critical range can be calculated using a table or formula. For a significance level of 0.05 and 3 degrees of freedom for the numerator and 60 degrees of freedom for the denominator, the q critical value is 3.480. Any pairwise comparison with a difference in means greater than this value would be considered statistically significant at the 0.05 level.

To learn more about section click here:brainly.com/question/12259293

#SPJ11