Question

A study of 50 individuals found mean systolic blood pressure $\bar{x} = 124.6$ mm Hg with sample standard deviation $S = 10.3$ mm Hg. Find the no. of individuals needed to reduce the standard error of the mean to 1 mm Hg.

• A. 54
• B. 51
• C. 107
• D. 106

Hint:

Always use $SE = \frac{S}{\sqrt{n}}$. To decrease SE, the sample size $n$ must be increased.

Answer 1

The Correct Option is D

Step 1: Recall the formula for Standard Error (SE).
The standard error of the mean is calculated as:
\[SE = \frac{S}{\sqrt{n}}\] where $S$ represents the sample standard deviation and $n$ is the sample size.
Step 2: Substitute the given values.
Given $SE = 1$ and $S = 10.3$.
\[1 = \frac{10.3}{\sqrt{n}}\] Step 3: Solve for $n$.
Rearranging the equation to solve for $\sqrt{n}$:
\[\sqrt{n} = \frac{10.3}{1} = 10.3\] Squaring both sides to find $n$:
\[n = (10.3)^2 = 106.09 \approx 106\] Step 4: Conclusion.
Therefore, a minimum of 106 individuals are needed to achieve a standard error of the mean of 1 mm Hg.
Final Answer:
\[\boxed{106}\]