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Brittany conducted a series of surveys to gather data on the ages of pet cats. The sample means for each survey are shown in the table.

\begin{tabular}{|c|c|}
\hline
Sample & \begin{tabular}{c}
Sample Mean \\
(years)
\end{tabular} \\
\hline
1 & 15.09 \\
\hline
2 & 14.45 \\
\hline
3 & 14.91 \\
\hline
4 & 15.09 \\
\hline
5 & 14.91 \\
\hline
6 & 15.82 \\
\hline
7 & 14.36 \\
\hline
8 & 15.55 \\
\hline
9 & 14.36 \\
\hline
10 & 15.27 \\
\hline
\end{tabular}

Use this information to complete the statements.

The average of the sample means is [tex]$\square$[/tex]. As the number of surveys conducted increases, the average of the sample means approaches the [tex]$\square$[/tex].



Answer :

GinnyAnswer
To find the average of the sample means, we first list out the sample means provided:

- 15.09
- 14.45
- 14.91
- 15.09
- 14.91
- 15.82
- 14.36
- 15.55
- 14.36
- 15.27

The average of the sample means can be found by summing all of these sample means and then dividing by the number of samples.

The sum of the sample means is:
[tex]\[ 15.09 + 14.45 + 14.91 + 15.09 + 14.91 + 15.82 + 14.36 + 15.55 + 14.36 + 15.27 \][/tex]

So, the sum calculated is:
[tex]\[ 149.81 \][/tex]

Next, we count the number of samples:
[tex]\[ 10 \][/tex]

The average of the sample means is therefore:
[tex]\[ \frac{149.81}{10} = 14.981 \][/tex]

So, the average of the sample means is:

[tex]\[ 14.981 \][/tex]

As the number of surveys conducted increases, the average of the sample means approaches the population mean.

Therefore, the completed statements are:

The average of the sample means is [tex]\(14.981\)[/tex]. As the number of surveys conducted increases, the average of the sample means approaches the population mean.