Two Groups of Patients with Colorectal Cancer Are Treated with a Different

Two groups of patients with colorectal cancer are treated with a different drug to reduce pain. A random
sample of 140 patients are treated using the drug Irinotican and a random sample of 127 patients are treated
using the drug Fluorouracil. Assume the two samples are random and independent. At α $\alpha$ = 0.01, test a
pharmaceutical representativeʹs claim that the difference between the mean number of pain-free months for
patients using Fluorouracil and the mean number of pain-free months for patients using Irinotican is less than
two months. $\begin{array} { l } \text {Fluorouracil}\\\mathrm { n } _ { 1 } = 127 \\\overline { \mathrm { x } } _ { 1 } = 8.5 \text { months } \\\sigma _ { 1 } = 1.5 \text { months }\end{array}$ $$\begin{array} { l } \text {Irinotican}\\\mathrm { n } _ { 2 } = 140 \\\bar { x } _ { 2 } = 10.3 \text { months } \\\sigma _ { 2 } = 1.2 \text { months }\end{array}$$