Question

In 2001, one county reported that, among 3132 white women who had babies, 94 were multiple births. There were also 20 multiple births to 606 black women. Does this indicate any racial difference in the likelihood of multiple births? Test an appropriate hypothesis and state your conclusion in context.

Answer 1

Hypothesis:

The ratio of ladies giving multiple birth to total number of women for any race will be the same.

Test:

Ratio of white women giving multiple births = 94 / 3132 = 0.0300

Ratio of black women giving multiple births = 20 / 606 = 0.0330

Conclusion:

There is no racial difference in the likelihood of multiple births. Although we do see a difference in the ratios calculated above, the difference is small enough to be due to sample size difference of white and black women. The smaller number of total black women makes the ratio calculated from this sample have a higher probability to deviate from what is expected. This deviation will account for the difference in probability between both races.

We can see the effects of this small sample size by increasing or decreases the numerator by 1 for black women:

21 / 606 = 0.0347

19 / 606 = 0.0313

This change in the data of one woman produces a very large percentage change in our ratio for black women (5%). Thus despite inaccuracy due to small sample size, our hypothesis is correct.