Patients with chronic kidney failure may be treated by dialysis, using a machine
ID: 3360007 • Letter: P
Question
Patients with chronic kidney failure may be treated by dialysis, using a machine that 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 45 dialysis patients and their average phosphorus level was 5.2 mg/dl.
a) Assuming blood phosphorus varies according to a normal distribution, with F = 0.9 mg/dl, find a 99% confidence interval for the mean blood phosphorus level for dialysis patients.
b) What is the margin of error in the 99% confidence interval found in part (a)
c) If the level of confidence is changed to 90%, and all the other parameters stay the same, what effect would lowering the level of confidence have in the size of the confidence interval? Explain.
d) How many dialysis patients should be sampled to obtain a margin of error of no more than 0.3 in a 99% confidence interval?
Explanation / Answer
WE ARE GIVEN that n = 45 , mean = 5.2 and sd = 0.9
we know that the margin of error is given as
MOE = z*sd/sqrt(n) , for 99% CI the value of Z is 2.58
2.58*0.9/sqrt(45) = 0.3461
now the confidence interval is given as
mean +- moe
5.2 +- 0.3461
=4.8539 5.5461
b) the margin of error is
MOE = z*sd/sqrt(n) , for 99% CI the value of Z is 2.58
2.58*0.9/sqrt(45) = 0.3461
c) for 90% CI the value of z is 1.645 , so the moe is
1.645*0.9/sqrt(45) = 0.2206
as the MOE reduces , the confidence interval reduces
d) again
2.58*0.9/sqrt(n) = 0.3, solving for n
(2.58*0.9/0.3)^2 = n
n = 59.90
= 60
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