Answer to Question #330717 in Statistics and Probability for Ken

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 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?

a. Formulate the null and alternative hypothesis in sentence and in symbol

b. Determine what test statistic to use

c. Compute the test statistic

d. Final answer

Answer 1

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

a. The null and alternative hypotheses are

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

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

c. 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

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

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