Chapter PVI, Problem 5RE

To determine

To explain do you think the same people used these two kiln sites and base your conclusion on a $95\%$ confidence interval for the difference in aluminum oxide content of pottery made at the sites.

Answer to Problem 5RE

We are $95\%$ confident that the mean difference in aluminum oxide content is between $-\text{3}\text{.43 and 1}\text{.71}$ and means in aluminum oxide content of the pottery made at the two sites could be reasonably the same.

Explanation of Solution

It is given in the question that archaeologists can use the chemical composition of clay found in pottery artifacts to determine whether sites were populated by the same ancient people. Thus, to find the confidence interval for mean we will use the calculator $\text{TI}-89$ . In the STAT Intsmenu, choose $4:2-$ SampTInt. You must specify if you are using data stored in two lists or if you will enter the means, standard deviations, and sizes of both samples. You must also indicate whether to pool the variances (when in doubt, say no) and specify the desired level of confidence. So, the list is as:

Ashley Rails	New forest
19.1	20.8
14.8	18
16.7	18
18.3	15.8
17.7	18.3

And the $\alpha =0.05$ so by using the calculator $\text{TI}-89$ , the result will be as:

  $\begin{array}{l}P=0.4547\\ \text{Margin of error}=2.5695\end{array}$

And the confidence interval will be as:

  $(-3.4295,1.7095)$ .

Based on the data, we are $95\%$ confident that the mean difference in aluminum oxide content is between $-\text{3}\text{.43 and 1}\text{.71}$ . Since the interval contains zero, the means in aluminum oxide content of the pottery made at the two sites could be reasonably the same.