A study is to be made of the relative effectiveness of two kinds of cough medicines in increasing sleep. Six people with colds are given medicine A the first night and medicine B the second night. It is assumed that medicine A does not affect the effectiveness of medicine B in the second night. Their hours of sleep each night are recorded. Subject 123456 MedicineA 7.2 7.7 7.8 6.9 7.9 8.4 MedicineB 5.9 5.2 7.0 6.0 7.1 8.5
Do these data provide sufficient evidence to prove a significant difference in the effectiveness of the two medicines? Test at the 5% level of significance. Based on your conclusion, what type of an error could you have possibly made? Give your answer in the context of the question