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).

5.4

5.2

4.4

4.8

5.7

6.4

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 = 0.8 mg/dl.

(a) Give a 95% confidence interval for the mean blood phosphorus level.

Answer 1

Solution:

We are given tha:

the data for one patient (in milligrams of phosphorus per deciliter of blood).

5.4

5.2

4.4

4.8

5.7

6.4

Thus n = 6

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 = 0.8 mg/dl.

We have to find a 95% confidence interval for the mean blood phosphorus level.

Formula:

where

zc is z critical value for c = 95% confidence level.

Find Area= ( 1 + c) /2 = ( 1 + 0.95 ) / 2 = 0.9750

Look in z table for area = 0.9750 and find corresponding z value.

z_c = 1.96

Thus

Thus lower and upper limits for confidence interval are:

where

Thus

Thus we are 95% confident that the true value of population mean blood phosphorus level is in between the limits: ( 4.6766 , 5.9568 )