Question

The National Center for Health Statistics reports that the mean systolic blood pressure for males 35 to 44 years of age is 128 mmHg and the standard deviation in this population is 15 mmHg. The medical director of a large company looks at the medical records of 72 executives in this age group and finds that the mean systolic blood pressure in this sample is x 126.07 mmHg. Find the power of a one sided test that the executives blood pressure is lower given the true mean is 124 mmHg, with ? 0.05

Answer 1

Hypotheses are:

$H_{0}:\mu=128,H_{a}:\mu<128$

The critical value of z for $\alpha=0.05$ is -1.645. The critical value of sample mean for which we will reject the null hypothesis is

$z=\frac{\bar{x}-\mu}{\sigma/\sqrt{n}}=\frac{\bar{x}-128}{15/\sqrt{72}}$

$-1.645=\frac{\bar{x}-128}{15/\sqrt{72}}$

$\bar{x}=125.092$

The z-score for $\bar{x}=125.092$ and $\mu=124$ is

$z=\frac{125.092-124}{15/\sqrt{72}}=0.62$

Power of the test is:

Power = P(z < 0.62) = 0.7324