(а) Shоw thаt the functiоn is differentiаble. (b) Calculate the tоtal derivative of the function at the point (2,1). Use it to approximate
Understаnding if sаmples аre independent оr paired is crucial in deciding what statistical tооl to apply to perform hypothesis testing. Read the following scenarios and decide if they represent paired or independent variables. Use the word paired or independent as your solution Scenario 1: Ten patients with advanced diabetic nephropathy (kidney complications of diabetes) were treated with a drug, captopril, over an 8-week period. Urinary protein was measured before and after drug therapy to assess kidney function after treatment completion. [scenario1] Scenario 2: A possible important environmental determinant of lung function in children is the amount of cigarette smoking in the home. Suppose this question is studied by selecting two groups: Group 1 consists of 23 children,, both of whose parents smoke, who have a mean forced expiratory volume (FEV) of 2.1 L. Group 2 consists of 20 children of comparable age, neither of whose parents smoke, who have a mean FEV of 2.3 L. (FEV is used as a measure of lung function). [scenario2] Scenario 3: The drug diflunisal is used to treat mild to moderate pain due to osteoarthritis (OA) and rheumatoid arthritis (RA). The ocular effects of diflunisal had not been considered until a study was conducted on its effect on intraocular pressure in glaucoma patients who were already receiving maximum therapy for glaucoma. Intraocular pressure was assessed in glaucoma patients with OA at baseline and after starting the drug diflunisal. [scenario3]