Researchers want to test a new hand exercise plan for arthritis patients to see if they have improved flexibility. They recruited 110 patients with arthritis in their hands and randomly assigned them to one of two treatment groups: group 1 took their regular medicine and did the new hand exercises; and group 2 only took medicine. After one month, 42 of the 55 in group 1 improved in their flexibility, and 37 of the 55 in group 2 improved their flexibility.

1. Random condition:

2. 10% condition:

3. Large Counts condition:

Are all the conditions for inference met?

All the conditions for inference, which include the Random Condition, 10% Condition, and Large Counts Condition, appear to be met in the study comparing a new hand exercise plan for arthritis patients.

Explanation:

To determine if all the conditions for inference are met in a study that compares a new hand exercise plan for arthritis patients, we assess the following conditions:

Random Condition: The researchers need to randomly assign patients to the treatment and control groups, which has been done in this study.
10% Condition: This condition states that the sample size must be less than 10% of the entire population. In most real-world studies, the population is large enough that this condition is met.
Large Counts Condition: This condition ensures that the expected number of successes and failures in each group is at least 10 to approximate the normal distribution. With 42 of 55 in group 1 and 37 of 55 in group 2 reporting improved flexibility, large counts condition is met.

Therefore, it appears that all the conditions for inference have been met in this study.