Question

Sampling the amount of a certain trace element in the blood of men and women have yielded different values based on the given data what is the likelihood that the population means of concentrations of the element are the same for men and women?

Random samples of 75 male and 50 female donors yield concentration means of 33 and 28 ppm, respectively.

Also, a standard deviation of 14.1 ppm (parts per million) for male blood donors and 14.1 ppm for female donors

Find the test statistics

Answer 1

Given,

$\small \bar{x}_1 = 33$,   $\small s_1 = 14.1$,   $\small n_1 = 75$

$\small \bar{x}_2 = 28$,   $\small s_2 = 14.1$,   $\small n_2 = 50$

we know that the test statistic is given by,

$\small z=\frac{(x_{1} - x_{2})} {\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}$

$\small z=\frac{(33 - 28)} {\sqrt{\frac{14.1^{2}}{75}+\frac{14.1^{2}}{50}}}$

$\small z=1.9423$