King Manuel I, Komnenus ruled the Byzantine Empire from Constantinople (Istanbul) during the years $1145$to $1180$A.D. The empire was very powerful during his reign, but declined significantly afterwards. Coins minted during his era were found in Cyprus, an island in the eastern Mediterranean Sea. Nine coins were from his first coinage, seven from the second, four from the third, and seven from a fourth. These spanned most of his reign. We have data on the silver content of the coins:

Did the silver content of the coins change over the course of Manuel’s reign?

Here are the means and variances of each coinage. The data are unbalanced.

Given in the question that Table of the silver content of the coins

We need to use Ti-83 calculator to test the silver content of the coins.

Do in the following way, click on STAT $\to$press $\to$EDIT, then put data into the list $L1,L2,L3$, and $L4$. The screenshot is given as below:

After that press STAT $\to$arrow over the TESTS $\to$arrow down to ANOVA $\to$Press var then select1, press var then select $2$, press var then select $3$and press var then select $4$to fill the values of $L1,L2,L3$, and L4. The screen shot is given as below:

The result of the calculation is shown below,

Analyzing the result of Ti-83 calculator it is clear that

$P$-value is $1.30$

The $5\%$level of significance of null hypothesis is rejected

Therefore, the mean silver content among the four coinages are different.