Chapter PVII, Problem 24RE

To determine

To explain is this evidence that human exposure to dioxin may result in the birth of more girls.

Answer to Problem 24RE

There is some evidence that human exposure to dioxin may result in the birth of more girls.

Explanation of Solution

It is given in the question that, a study published in the journal environmental health perspectives examined the gender ratios of children born to workers exposed to dioxin. Let us assume all the conditions and assumptions are met for inference. Thus, to find out any test for proportion we will use the calculator $\text{TI}-89$ . Then select $5:1-$ PropZTest from the STAT TESTSmenu. Specify the hypothesized proportion. Enter the observed value of x . Specify the sample size. Indicate what kind of test you want: one-tail lower tail, two-tail, or one-tail upper tail. Specify whether to calculate the result or draw the result. So, the hypothesis is defined as:

  $\begin{array}{l}{H}_0:p=0.512\\ H_0:p<0.512\end{array}$

So, it is a lower tail test. And we have,

  $\begin{array}{l}\widehat{p}=0.40\\ n=227\end{array}$

Thus, by using the calculator $\text{TI}-89$ , the test statistics and the P-value is as:

  $\begin{array}{l}z=3.38\\ P=0.0004\end{array}$

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

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

Thus, we conclude that there is some evidence that human exposure to dioxin may result in the birth of more girls.