Question

1. a group of math teachers in the district are considering a new format for their summative assessments, but they do not know if students will be more successful on the new format or the old format. they will randomly assign half of the math students to the new format and half of the students to the old format. there are 204 students. a) design a completely randomized experiment the teachers can use.

Explanation:

1. Label students: Assign each of the 204 students a unique number from 1 to 204.
2. Random assignment: Use a random number generator (or a random number table). Generate 102 distinct random numbers in the range of 1 - 204. The students corresponding to these 102 numbers will be assigned to the new - format assessment group.
3. Treatment and control: The group of 102 students with the randomly - selected numbers will take the new - format summative assessment (treatment group), and the remaining 102 students will take the old - format summative assessment (control group).
4. Data collection: After the assessments, collect the scores of all students.
5. Analysis: Compare the average scores (or other relevant statistical measures) of the two groups. If the average score of the new - format group is significantly higher (using an appropriate statistical test, such as a t - test for two independent samples if the data is approximately normally distributed), it can be inferred that students may be more successful with the new format. If there is no significant difference, the teachers may need to consider other factors or further experimentation.

Answer:

1. Label each of the 204 students with a unique number from 1 to 204.
2. Use a random number generator (or random number table) to select 102 distinct numbers in the range 1 - 204.
3. Assign the students with the selected numbers to the new - format assessment (treatment group) and the remaining students to the old - format assessment (control group).
4. Administer the assessments and collect scores.
5. Compare the scores (e.g., using a t - test if appropriate) to determine if there is a significant difference between the two groups.