Statistics

(8). Randomly select 20 individuals who have problem with sleeping. The 20 individuals were randomly assigned to two groups: treatment group (group 1) and control group (group 2). Individuals in control group were given placebo (vitamin pills). Individual in treatment group take a new medicine which is stated to improve sleeping. After two weeks their overnight sleeping time (in hours) were recorded as the following: treatment group: 6, 7, 5, 6, 6, 4, 5, 5, 6, 7. control group: 4, 3, 5, 4, 6, 3, 5, 6, 6, 5. Let /1, /2 be the population mean overnight sleeping times for treatment group and control group, respectively. Assume two samples are independent, both from normal populations with standard deviation 01 = 1.5, 02 = 2.8. Do a hypothesis test to determine if the medicine help people sleep longer at the significant level 0.05. Solve by reject region method