The effectiveness of the new drug for treatment of headaches is investigated in clinical trial. New drug is administered at two dosages: 5 milligrams and 10 milligrams. These are denoted as N05 and N10. Superficial properties of medications are identical. Female and male patients are arbitarily assigned to get one of the two new dosages. After one month patients complete quality-of-life (QOL) questionnaire. QOL scores are on a 100 point scale. Standardized mean score is 50. Higher scores point to a better quality of life. Results for QOL of clinical trial are in table below.
Treatment N05 + male: 50 46 69 72 70 47 63 68
Treatment N05 + female: 49 42 25 70 46 56 62 42
Treatment N10 + male: 61 52 65 54 58 55 61 58
Treatment N10 + female: 62 62 59 75 64 76 73 59
a. Test claim that mean responses are same for all populations of patients receiving either treatment and of either gender.
b. If mean responses are not all equal, test claim that there is no interaction between kinds of treatment and sex.
c. If there is significant interaction find out which treatment-sex combination has highest mean quality-of-life score. Find out which other combinations, if any, have means that are not significantly different from highest. Set &=0.05.
d. If there is no significant interaction, test claim that expected mean quality-of-life score is same for both dosages.
e. If there is no significant interaction, test claim that mean quality-of-life score is same for females and males.