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
The null and alternative hypotheses are
Because 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 , 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
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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