Question

The mean serum-creatinine level measured in 12 patients 24 hours after they received a
newly proposed antibiotic was 1.2 mg/dL. If the mean and standard deviation of serum
creatinine in the general population are 1.0 and 0.4 mg/dL, respectively, then, using a
significance level of .05, test whether the mean serum-creatinine level in this group is
different from that of the general population.

Answer 1

Null hypothesis $H_0:\mu=1.0.$

Alternative hypothesis $H_a:\mu\ne1.0.$

Test statistic: $z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}=\frac{1.2-1.0}{\frac{0.4}{\sqrt{12}}}=1.73.$

P-value: $p=2P(Z>1.73)=0.0836.$

Since the P-value is greater than 0.05, fail to reject the null hypothesis.

There is no significant evidence that the mean serum-creatinine level in this group is

different from that of the general population.