Chapter PVI, Problem 9RE

To determine

To explain is there any evidence that U.S. babies and Australian babies do not weigh the same amount at birth if we believe the Missouri babies fairly represent American newborns.

Answer to Problem 9RE

Yes, American babies are different from Australian babies in birth weight.

Explanation of Solution

It is given in the question that the national perinatal statistics unit of the Sydney children’s hospital reports that the mean weight of the all babies born in Australia was $3361$ grams about $7.41$ pounds. Thus, to test the hypothesis for mean we will use the calculator $\text{TI}-89$ . In the STAT Tests menu, choose $2:$ T -Test. You must specify whether you are using data stored in a list or whether you will enter the mean, standard deviation, and size of your sample. You must also specify the hypothesized model mean and whether the test is to be two-tail, lower-tail, or upper-tail. Select whether the test is to be simply computed or whether to display the distribution curve and highlight the area corresponding to the P-value of the test. Thus, let us define the hypothesis as:

  $\begin{array}{l}{H}_0:\mu =7.41\\ H_a:\mu \ne 7.41\end{array}$

And also,

  $\begin{array}{l}\overline{x}=7.68\\ n=112\\ s=1.31\end{array}$

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

  $\begin{array}{l}t=2.18\\ P=0.0313\end{array}$

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 Missouri babies fairly represent the U.S. these data suggest that American babies are different from Australian babies in birth weight and it appears American babies are heavier on average.