A randomized trial is conducted to evaluate the effectiveness of a newly developed treatment for joint pain in patients with arthritis. The treatment is compared to an established treatment that has been shown to be effective. Two hundred patients with arthritis agree to participate and are randomly assigned to either the newly developed treatment or to the established treatment. Among the several clinical outcomes in the investigation we focus on a secondary outcome, quality of life (QOL). QOL scores (ranging from O to 100, with higher scores indicative of better QOL) are measured on each patient. The following data are observed:

Treatment No. of Patients Mean QOL SD QOL

Newly developed 100 80.2 5.7

Established 100 75.4 6.1

a.Construct a 95% confidence interval for the difference in mean QOL scores between treatments.

b.Based on (a), is there a significant difference in mean QOL scores between treatments? Justify your answer.