The two samples whose statistics are given in the table thought to come from populations with
Equal variances. What is the pooled estimate of the population standard deviation? $$\begin{array} { | c | c | c | }
\hline n & \text { Mean } & \text { SD } \
\hline 50 & 22 & 3 \
\hline 55 & 25 & 4 \
\hline
\end{array}$$
A) 3.50
B) 3.56
C) 1.87
D) 5.00
E) 3.52

Question

The two samples whose statistics are given in the table thought to come from populations with
Equal variances. What is the pooled estimate of the population standard deviation? $$\begin{array} { | c | c | c | } 
\hline n & \text { Mean } & \text { SD } \
\hline 50 & 22 & 3 \
\hline 55 & 25 & 4 \
\hline
\end{array}$$
A) 3.50
B) 3.56
C) 1.87
D) 5.00
E) 3.52

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: $\sqrt{\frac{(50-1)3^2 + (55-1)4^2}{50+55-2}} = \sqrt{\frac{49 \times 9 + 54 \times 16}{103}} = \sqrt{\frac{441 + 864}{103}} = \sqrt{\frac{1305}{103}} \approx 3.56$.

The Two Samples Whose Statistics Are Given in the Table n Mean SD 5022355254\begin{array} { | c | c | c | } \hline n & \text { Mean } & \text { SD } \\\hline 50 & 22 & 3 \\\hline 55 & 25 & 4 \\\hline\end{array}n5055​ Mean 2225​ SD 34​​

The Two Samples Whose Statistics Are Given in the Table $\begin{array} { | c | c | c | } \hline n & \text { Mean } & \text { SD } \\\hline 50 & 22 & 3 \\\hline 55 & 25 & 4 \\\hline\end{array}$