Question

The claim is that the white blood cell counts of adult females are normally? distributed, with a standard deviation equal to 1.631.63. a random sample of 38 adult females has white blood cell counts with a mean of 7.43 and a standard deviation of 3.07. find the value of the test statistic.

Answer 1

From the question, we know the population standard deviation, σ = 1.63, the sample standard deviation, s = 3.07, the sample mean, $\bar{x}=7.43$ and the sample size, n = 38.

The question illustrates a hypothesis chi-square test of variance.

The test statistics for a Chi-squared test of variance is given by
$T=(n-1)\left( \frac{s}{\sigma} \right)^2 \\ \\ =(38-1)\left( \frac{3.07}{1.63} \right)^2 \\ \\ =37(1.883)^2=37(3.5473) \\ \\ =131.25$