Question #330713

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



1
Expert's answer
2022-04-20T03:20:56-0400

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


The null and alternative hypotheses are

H0:μ=7250,H1:μ<7250.H_0:\mu=7250,\\ H_1:\mu<7250.


Because σ\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 α=0.01\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=xˉμs/n=485072502500/15=3.718<2.624.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.


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