Question

Patients with chronic kidney failure may be treated by dialysis, in which a machine removes toxic wastes from the blood, a function normally performed by the kidneys. Kidney failure and dialysis can cause other changes, such as retention of phosphorus, that must be corrected by changes in diet. A study of the nutrition of dialysis patients measured the level of phosphorus in the blood of several patients on six occasions. Here are the data for one patient (in milligrams of phosphorus per deciliter of blood). 5.3 5.2 4.6 4.9 5.8 6.2 The measurements are separated in time and can be considered an SRS of the patient's blood phosphorus level.

Assume that this level varies Normally with σ = 0.9 mg/dl. (Round your answers to three decimal places.) (a) Give a 95% confidence interval for the mean blood phosphorus level.

Answer 1

Solution :

Given that,

= = (5.3 + 5.2 + 4.6 + 4.9 + 5.8 + 6.2) / 6 = 32 / 6 = 5.333

Z_/2 = 1.96

Margin of error = E = Z_/2* ( /n)

= 1.96 * (0.9 / 6)

= 0.720

At 95% confidence interval estimate of the population mean is,

- E < < + E

5.333 - 0.720 < < 5.333 + 0.720

4.613 < < 6.053

(4.613 , 6.053)