Answer to Question #344331 in Statistics and Probability for Maybel

Question

The mean serum-creatinine level measured in 10 patients 24 hours after they received a

newly proposed antibiotic was 1.2 mg/dL with standard deviation of 0.4mg/dL. If the serum level in the general population is 1.0mg, test the hypothesis that the serum level in this group is different from that of the general population. Use significant significant level of 0.05

Answer 1

The following null and alternative hypotheses need to be tested:

$H_0:\mu=1$

$H_1:\mu\not=1$

This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

Based on the information provided, the significance level is $\alpha = 0.05,$ and the critical value for a two-tailed test is $z_c = 1.96.$

The rejection region for this two-tailed test is $R = \{z:|z|>1.96\}.$

The z-statistic is computed as follows:

$$z=\dfrac{\bar{x}-\mu}{\sigma/\sqrt{n}}=\dfrac{1.2-1}{0.4/\sqrt{10}}\approx1.5811$$

Since it is observed that $|z|=1.5811<1.96=z_c,$ it is then concluded that the null hypothesis is not rejected.

Using the P-value approach:

The p-value is $p=2P(z>1.5811)= 0.113855,$ and since $p= 0.113855>0.05=\alpha,$ it is concluded that the null hypothesis is not rejected.

Therefore, there is not enough evidence to claim that the population mean $\mu$

is different than 1, at the $\alpha = 0.05$ significance level.