Question
A scientist simulates chance outcomes by randomly re-sorting treatment groups one hundred times and constructing a distribution of the response variable means for each treatment group. What can the scientist predict about the means of the treatment group distributions?
A. The means of the treatiment group distitutions will be very diferent tom the response varabie mean dite entre population.
B. The means of the treatment group disticutions will de exacty me same
C. The means of the treatment group will be very different
D. The means of the treatment group distributions will be very close to each other and close to the mean of the entire population.
The scores for an online exam for a class of 30 students were randomly split into two groups of equal size, Group A and Group B. Group A had a mean score of 91%. It was then found that the entire class had a mean score of 88%. What can be said about the mean score for Group B?
A. The mean score for Group B will be higher than the mean score for the entire class.
B. The mean score for Group B will be lower than the mean score for the entire class.
C. The mean score for Group B will be the same as the mean score for Group A.
D. The mean score for Group B will be equal to the mean score for the entire class.
The range of response variable measures for a treatment group sampled from a population equals 8. Which of the following could represent the range of response variable measures for the population?
A. 2
B. 12
C. 8
D. 6
If the members of the group {73, 49,32, 84, 39, 63, 22, 12, were randomly assigned to two groups, then each group's range would need to be less than what value?
A. 44
B. 46.75
C. 72
D. 61
If the members of the group {94, 37, 19, 48, 93, 36, 22, 23, were randomly assigned to two groups, around what value would each group's mean be symmetrical?
A. 46.75
B. 46.5
C. 94
D. 71
A. The means of the treatiment group distitutions will be very diferent tom the response varabie mean dite entre population.
B. The means of the treatment group disticutions will de exacty me same
C. The means of the treatment group will be very different
D. The means of the treatment group distributions will be very close to each other and close to the mean of the entire population.
The scores for an online exam for a class of 30 students were randomly split into two groups of equal size, Group A and Group B. Group A had a mean score of 91%. It was then found that the entire class had a mean score of 88%. What can be said about the mean score for Group B?
A. The mean score for Group B will be higher than the mean score for the entire class.
B. The mean score for Group B will be lower than the mean score for the entire class.
C. The mean score for Group B will be the same as the mean score for Group A.
D. The mean score for Group B will be equal to the mean score for the entire class.
The range of response variable measures for a treatment group sampled from a population equals 8. Which of the following could represent the range of response variable measures for the population?
A. 2
B. 12
C. 8
D. 6
If the members of the group {73, 49,32, 84, 39, 63, 22, 12, were randomly assigned to two groups, then each group's range would need to be less than what value?
A. 44
B. 46.75
C. 72
D. 61
If the members of the group {94, 37, 19, 48, 93, 36, 22, 23, were randomly assigned to two groups, around what value would each group's mean be symmetrical?
A. 46.75
B. 46.5
C. 94
D. 71
Answers
GPT-4o mini
Let's address each question one by one:
1. **About the means of treatment group distributions**:
The best choice is:
**D. The means of the treatment group distributions will be very close to each other and close to the mean of the entire population.**
This is because if the scientist is randomly re-sorting the treatment groups and simulating chance outcomes, the means of the treatment groups should converge around the overall population mean due to the law of large numbers.
2. **Mean score for Group B**:
The best option is:
**B. The mean score for Group B will be lower than the mean score for the entire class.**
Since Group A has a mean of 91%, which is higher than the class mean of 88%, and both groups combined must equal the total class mean, Group B must have a mean lower than 88% to balance out the higher mean of Group A.
3. **Range of response variable measures for the population**:
The correct choice is:
**B. 12**
The range for a sample can be less than or equal to the range of the entire population. Since the treatment group has a range of 8, the true population range could be larger than that, making 12 a reasonable estimation.
4. **Range of groups formed from the set {73, 49, 32, 84, 39, 63, 22, 12}**:
The largest value is 84 and the smallest is 12, so the overall range is 84 - 12 = 72. Each group's range would need to be less than half of the total range. Thus, the maximum each group's range should be less than is:
**C. 72** (but technically it should be less than 72; if they need to have different ranges, the highest possible range for either would be less than 72.)
5. **Symmetrical mean for groups from {94, 37, 19, 48, 93, 36, 22, 23}**:
To find the symmetrical mean, first calculate the average of the numbers in the set. The total sum is \(94 + 37 + 19 + 48 + 93 + 36 + 22 + 23 = 372\) and there are 8 numbers. Dividing gives:
\(372 / 8 = 46.5\).
Therefore, the symmetrical mean for the two groups would be:
**B. 46.5**.
If you have any further questions or another topic to discuss, feel free to ask!
1. **About the means of treatment group distributions**:
The best choice is:
**D. The means of the treatment group distributions will be very close to each other and close to the mean of the entire population.**
This is because if the scientist is randomly re-sorting the treatment groups and simulating chance outcomes, the means of the treatment groups should converge around the overall population mean due to the law of large numbers.
2. **Mean score for Group B**:
The best option is:
**B. The mean score for Group B will be lower than the mean score for the entire class.**
Since Group A has a mean of 91%, which is higher than the class mean of 88%, and both groups combined must equal the total class mean, Group B must have a mean lower than 88% to balance out the higher mean of Group A.
3. **Range of response variable measures for the population**:
The correct choice is:
**B. 12**
The range for a sample can be less than or equal to the range of the entire population. Since the treatment group has a range of 8, the true population range could be larger than that, making 12 a reasonable estimation.
4. **Range of groups formed from the set {73, 49, 32, 84, 39, 63, 22, 12}**:
The largest value is 84 and the smallest is 12, so the overall range is 84 - 12 = 72. Each group's range would need to be less than half of the total range. Thus, the maximum each group's range should be less than is:
**C. 72** (but technically it should be less than 72; if they need to have different ranges, the highest possible range for either would be less than 72.)
5. **Symmetrical mean for groups from {94, 37, 19, 48, 93, 36, 22, 23}**:
To find the symmetrical mean, first calculate the average of the numbers in the set. The total sum is \(94 + 37 + 19 + 48 + 93 + 36 + 22 + 23 = 372\) and there are 8 numbers. Dividing gives:
\(372 / 8 = 46.5\).
Therefore, the symmetrical mean for the two groups would be:
**B. 46.5**.
If you have any further questions or another topic to discuss, feel free to ask!