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) 7.22
B) 7.14
C) 7
D) 2.65
E) 10

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) 7.22
B) 7.14
C) 7
D) 2.65
E) 10

Quizplus · Accepted Answer

The pooled standard deviation is calculated using the formula: $\sqrt{\frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2}}$. Substituting the given values: $\sqrt{\frac{(12-1)6^2 + (16-1)8^2}{12+16-2}} = \sqrt{\frac{11 \times 36 + 15 \times 64}{26}} = \sqrt{\frac{396 + 960}{26}} = \sqrt{\frac{1356}{26}} = \sqrt{52.15} \approx 7.22$.

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 $\begin{array} { | c | c | c | } \hline n & \text { Mean } & \text { SD } \\\hline 12 & 45 & 6 \\\hline 16 & 41 & 8 \\\hline\end{array}$