Chapter 10, Problem 32PT3

(a)

To determine

To find: that this is and observational study or experiment study.

Answer to Problem 32PT3

Observational study, because the experimenters are unable to monitor the variables that can lead to a handicapped person

Explanation of Solution

The experimenters have no control over whether or not a baby without major handicaps will withstand. This is an observational study that is whether or not the researchers have influence over the experiment is the distinction between an observational study and an experimental study.

(b)

To determine

To Explain: the suitable statistical proof to clarify the answer.

Explanation of Solution

Given:

  $\begin{array}{l}{X}_1=179\\ n_1=242\\ X_2=193\\ n_2=233\end{array}$

Calculation:

null and alternative hypothesis

  $\begin{array}{l}{H}_0:P_1=P_2\\ H_1:P_1<P_2\end{array}$

  $\begin{array}{l}Z=\frac{{\widehat{P}}_1-{\widehat{P}}_2}{\sqrt{\widehat{P}\left(1-\widehat{P}\right)\left(\frac{1}{n_1}+\frac{1}{n_2}\right)}}\\ \widehat{P}=\frac{X_1+X_2}{n_1+n_2},{\widehat{P}}_1=\frac{X_1}{n_1},{\widehat{P}}_2=\frac{X_2}{n_2}\end{array}$

  $\begin{array}{l}\widehat{P}=0.78316\\ {\widehat{P}}_1=0.73967\\ {\widehat{P}}_2=0.828333\end{array}$

The Test Statistic,

  $Z=-2.344$

  $Z_{\alpha }=-1.645$

Finding the critical region, because the level of significance is not provided, using 0.05. This is a left tailed test, will not divide alpha by 2.

  $Z<Z_{\alpha }\Rightarrow reject{H}_0$

There should be dismiss the null hypothesis because the test statistics fell below the critical value. There is ample evidence to suggest that the VLBW group graduation rate is substantially lower than that of standard birth weight controls.