Chapter PV, Problem 15RE

To determine

To explain does this indicate an increase in the incidence of early births of twins and test an appropriate hypothesis and state your conclusion.

Answer to Problem 15RE

There is no evidence of an increase in the incidence of early births of twins.

Explanation of Solution

It is given in the question that there is some indication in medical literature that doctors may have become more aggressive in inducing labor or doing preterm cesarean sections when a women is carrying twins. Thus, to calculate an appropriate hypothesis we will use $\text{TI}-89$ calculator. Thus, for this first we have to select $6:2-\text{PropZInt}$ from the STAT TESTS menu. Then, enter the observed counts and sample sizes for both the samples. Then we will indicate what kind of test we want: one-tail lower tail, two-tail, or one-tail upper tail. Then, we will specify whether to calculate the result or draw the result. Hence we have,

  $\begin{array}{l}{x}_1=20\\ n_1=43\\ x_2=26\\ n_2=48\\ \alpha =0.05\\ H_0:p_1=p_2\\ H_a:p_1<p_2\end{array}$

So, by putting the values above by using the calculator we will get the result as,

The P-value will be then,

  $P=0.2329$

And as we know if the P-value is smaller than the significance level, then reject the null hypothesis, so, we have,

  $P<0.05\Rightarrow \text{ Reject }{H}_0$

Thus, we conclude that there is no evidence of an increase in the incidence of early births of twins.