Chapter PVI, Problem 18RE

To determine

To explain is this evidence that the rate of cesarean births in the two states different.

Answer to Problem 18RE

There is insufficient evidence that the rate of cesarean births in the two states different.

Explanation of Solution

It is given in the question that some people fear that differences in insurance coverage can affect healthcare decisions. Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator $\text{TI}-89$ . Then select $6:2-$ PropZTestfrom the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded. Now, we know that the test is two tailed and the hypothesis is defined as:

  $\begin{array}{l}{H}_0:p_{\text{1}}-p_{\text{2}}=0\\ H_a:p_{\text{1}}-p_{\text{2}}\ne 0\end{array}$

And also we know that,

  $\begin{array}{l}{p}_1=0.166\\ n_1=223\\ p_2=0.188\\ n_2=186\end{array}$

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

  $\begin{array}{l}z=-0.58\\ P=0.5607\end{array}$

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,

  $P>0.05\Rightarrow \text{Fail to Reject }{H}_0$

Thus, we conclude that there is insufficient evidence that the rate of cesarean births in the two states different.