Answer to Question #110341 in Statistics and Probability for Kasey Z

Question

The mean blood pressure of a large population of adult males is 200 mmHg with a standard deviation of 20 mmHg. Assume that blood pressure measurements are normally distributed. (a) What is the probability that a sample of 100 men from this age group will have mean blood pressure below 204 mmHg? (b) If a group of 25 older men who are strict vegetarians have a mean blood pressure of 188 mmHg, would you say that vegetarianism significantly lowers blood blood levels?

Answer 1

Based on the central limit theorem, the sample mean is distributed as a normal distribution with mean 200 mmHg and a standard deviation $20/ \sqrt{100}=2$ mmHg.

$$P(X<204)=P(Z<{204-200\over2})=P(Z<2)\approx0.977250$$

$H_0:\mu=200$

$H_1:\mu<200$

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

$$z={\bar{X}-\mu \over \sigma/\sqrt{n}}={188-200 \over 20/\sqrt{25}}=-3$$

The p-value is $p=0.00135$ and since $p=0.00135<0.05,$ it is concluded that the null hypothesis is rejected. Therefore, there is enough evidence to claim that the population $\mu$  is less than 200, at the 0.05 significance level.

We may say that vegetarianism significantly lowers blood levels.