Question

Medical literature tells us that our blood is mainly composed of red and white corpuscles and a normal human body must average 〖7250/mm〗^3 of white blood cell counts. If a sample of 15 individuals chosen at random from a certain place has an average of 〖4850/mm〗^3 with a standard deviation of 〖2500/mm〗^3, would you say that the people in that place have low white blood cell counts?

This is the questions:

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

b.Determine what test statistic to use.

c.Compute the test statistic.(Show neat and complete solution)

Answer 1

(a) Null hypothesis, H₀, is that held by medical literature (μ=count 7250/mm³ white cells) and applying to all places.

Alternative hypothesis, H_A, is that μ≠7250/mm³. (Not the specific value 4850/mm³.)

(b) Test statistic is the mean of the sample, μ, indicative of the population mean. Is it significantly different from what the books say?

(c) The sample standard deviation has to be adjusted because of the sample size 15. σ for the population is estimated from the sample standard deviation=2500/√15=645.5/mm³. The sample size gives us the number of degrees of freedom (DOF) to apply=15-1=14 and we use t-distribution tables to determine the critical value. We also need to know the significance level or confidence level to be applied. If the confidence level is 95%, the significance level is 5%. No significance level has been given.

If we assume 95% is a sufficient confidence level, then, since H_A is μ≠7250/mm³, we are testing for less than or greater than, which is a two-sided approach so 95% has to cover both sides of the mean and the significance level is halved to 2.5%. The t-distribution table gives 2.145 as the critical value of standard deviations from the mean when DOF=14. The difference between 7250 and 4850=2400/mm³, which is 2400/645.5=3.72 standard deviations from the mean, exceeding the critical value. We conclude that H₀ is to be rejected, so we're reasonably confident that the average white cell count is not 7250/mm³.