Question

In 2004​, one county reported that among 3116 white women who had​ babies, 139 were multiple births. There were also 23 multiple births to 607 black women. Does this indicate any racial difference in the likelihood of multiple​ births? ​a) Test an appropriate hypothesis and state your conclusion. ​b) If your conclusion is​ incorrect, which type of error did you​ commit? ​a) Let p1 be the proportion of multiple births for white women and  p2 be the proportion of multiple births for black women. Choose the correct null and alternative hypotheses below.

Answer 1

Claim : There is difference in the likelihood of multiple​ births

H0 : P1 = P2   vs Ha : P1 ≠ P2   

Given : x1 = 139, x2 = 23, n1 = 3116 , n2 = 607 , 1 = x1 /n1 = 0.0446, 2= x2 /n2 = 0.0379 , 1 = 1 – 1 = 0.9554 , 2 = 1 – 2 = 0.9621

Test statistic :

Z =

p =     ; q =1 – p

p =

p = 0.0435

q = 1 - 0.0435 = 0.9565

Z =

Z = 0.74

P value = 2*[1- P( z < 0.74 )] = 2*0.2297  

P value = 0.4593

Assume α =0.05

As P value is greater than 0.05, we do not reject H0.

There is no significant evidence that the difference in the likelihood of multiple​ births.

Type II error : We do not reject the null H0, when actually it is false.

So you could commit type II error .