The two samples whose statistics are given in the table are thought to come from populations with
Equal variances. What is the pooled estimate of the population standard deviation? $$\begin{array} { | c | c | c | }
\hline n & \text { Mean } & \text { SD } \
\hline 12 & 45 & 6 \
\hline 16 & 41 & 8 \
\hline
\end{array}$$
A) 10
B) 2.65
C) 7.14
D) 7.22
E) 7

Question

The two samples whose statistics are given in the table are thought to come from populations with
Equal variances. What is the pooled estimate of the population standard deviation? $$\begin{array} { | c | c | c | } 
\hline n & \text { Mean } & \text { SD } \
\hline 12 & 45 & 6 \
\hline 16 & 41 & 8 \
\hline
\end{array}$$
A) 10
B) 2.65
C) 7.14
D) 7.22
E) 7

Quizplus · Accepted Answer

The pooled estimate of the population standard deviation is given by the formula:$$s_p = \sqrt{\frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1 + n_2 - 2}}$$where $n_1$ and $n_2$ are the sample sizes, $s_1$ and $s_2$ are the sample standard deviations.Plugging in the values from the table, we get:$$s_p = \sqrt{\frac{(12-1)6^2 + (16-1)8^2}{12 + 16 - 2}} = 7.22$$Therefore, the pooled estimate of the population standard deviation is 7.22.

The Two Samples Whose Statistics Are Given in the Table n Mean SD 1245616418\begin{array} { | c | c | c | } \hline n & \text { Mean } & \text { SD } \\\hline 12 & 45 & 6 \\\hline 16 & 41 & 8 \\\hline\end{array}n1216​ Mean 4541​ SD 68​​

The Two Samples Whose Statistics Are Given in the Table $\begin{array} { | c | c | c | } \hline n & \text { Mean } & \text { SD } \\\hline 12 & 45 & 6 \\\hline 16 & 41 & 8 \\\hline\end{array}$