Question

A study of the nutrition of dialysis patients measured the level of phosphorus in the blood of a patient on 30 occasions. The mean phosphorus level for this patient was 5.2 mg/dL and a population standard deviation for all dialysis patients of 1.0 mg/dL. Is there evidence that this patient’s true mean phosphorus level significantly exceeds 4.8 mg/dL, the upper end of the “normal” range? 5.

For the story above,

(a) state the hypotheses,

(b) calculate the test statistic and p-value, and

(c) state your conclusion in terms of the story. Provide the SPSS function used to calculate the p-value.

Answer 1

a) Claim: Patient’s true mean phosphorus level significantly exceeds 4.8 mg/dL.

The null and alternative hypothesis is

$H1:\mu> 4.8$

Here population standard deviation is known so we have to use z-test statistic.

Sample size = n = 30

Sample mean = $\bar{x}$ = 5.2

Population standard deviation = $\sigma$ = 1

b) Test statistic is

$z =\frac{\bar{x}-\mu }{\sigma /\sqrt{n}}$

$z =\frac{5.2-4.8 }{1 /\sqrt{30}}=\frac{0.4}{0.182574}=2.19$

Level of significance = 0.05

P-value = 0.0142

c) P-value < 0.05 we reject null hypothesis.

Conclusion: patient’s true mean phosphorus level significantly exceeds 4.8 mg/dL.