Answer to Question #330713 in Statistics and Probability for Clouds

Question

Medical literature tells us that our blood is mainly composed of red and white blood cells corpuscles and a normal human body must average 7250/mm³ of white blood cells counts. If a sample of 15 individuals chosen at a random from a certain place has an average of 4850/mm³ with a standard deviation of 2500/mm³ would you say that the people in that place have low white blood cell counts

Answer 1

$\mu=7250, \ n=15, \ \bar{x}=4850, \ s=2500.$

The null and alternative hypotheses are

$H_0:\mu=7250,\\ H_1:\mu<7250.$

Because $\sigma$ is unknown and the population is normally distributed, we use the t-test.

The test is a left-tailed test, let's take the level of significance is $\alpha=0.01$ , the degrees of freedom are d.f. = 15 - 1 = 14. So, using t-table, the critical value is t₀ = - 2.624. The rejection region is t < -2.624. The standardized test statistic is

$t=\cfrac{\bar{x}-\mu}{s/\sqrt{n}}=\cfrac{4850-7250}{2500/\sqrt{15}}=-3.718<-2.624.$

Because t is in the rejection region, we reject the null hypothesis, the people in that place have low white blood cell counts.