For a shoulder injure the average recovery time is 16 weeks. The doctor recommended physical therapy 3 times a week, but with a full time job, full time school, and full time family schedule, making it to physical therapy 3 days a week can be really challenging. I have been wondering what would happen to the recovery time if physical therapy was reduced to 2 days a week instead of 3 days per week. By only doing physical therapy 2 days a week instead of 3, it will lengthen the recovery time. The null hypothesis would be that changing the amount of physical therapy would not lengthen the recovery time (H0: μ = 16). The alternate hypothesis would be that changing the physical therapy schedule would change the recovery time (HA: μ ≠ 16). A Type II error could occur if I accepted the null hypothesis that changing my physical therapy would not lengthen my recovery time when in fact it added time to my recovery. A type I error can occur if the investigator rejects a null hypothesis that is actually true. A type II error occurs if the investigator fails to reject a null hypothesis that is actually false. While type I and type II errors can not be completely avoided, they can be reduced by increasing the sample size
Using the above scenario what would be the level of significance, and why?