Question

Substance X is found in the bloodstream of humans. A random sample of 75 males had a mean content of 28 ppm of Substance X in their blood. A random sample of 50 females had a mean content of 33 ppm of Substance X in their blood. The population standard deviations for males and females are known to be 14.1 ppm and 9.5 ppm, respectively. Use the 88.12% degree of confidence. An appropriate set of null and alternative hypotheses to test whether males and females have the same amount of Substance X in their blood is:

Answer 1

H0: u1 - u2 = 0

H1: u1 - u2 ≠ 0

Explanation:

This question requires us to state the hypothesis to be used for this test to know if males and females have the same amount of substance X. I have gone further to also calculate the test statistics too.

Null hypothesis:

H0: u1 - u2 = 0

Alternative hypothesis:

H1: u1 - u2 ≠ 0

X1 = 28, sd1 = 14.1, n1 = 75

X2 = 33, sd2 = 9.5, n2 = 50

We have a 2 tailed test

Alpha = 1-0.8812

= 0.1188

Critical value = 1.56

If z<-1.56 or z>1.56

Reject null hypothesis

Test statistic

= (28-33)/14.1²/75 + 9.5²/50

= -2.37

Therefore we reject the H0 because -2.37 is less than -1.56