Q. 59 - The Practice of Statistics for AP

Question

59.Blood pressure A medical study finds that $\overline{x}=114.9$ and $S_x= 21.88$ for the seated systolic blood pressure of the $27$ members of one treatment group. What is the standard error of the mean? Interpret this value in context.

Step-by-Step Solution

Answer

The standard error of the mean is $1.789$.

Step 1: Given information

A medical study finds $\overline{x}=114.9$ and $S_x= 21.88$ for the seated systolic blood pressure of the $27$ members of one treatment group.

Step 2: Explanation

Utilizing the formula, $\overline{E}=\frac{s_x}{\sqrt{n}}$, determine the standard error of mean. Where, Mean $\overline{x}$ is $114.9$, the standard deviation $s_x$ is $9.3$, and the sample size $n$is $27.$

$\overline{E}=\frac{s_x}{\sqrt{n}}$

$=\frac{9.3}{\sqrt{27}}$

$=1.789$

Therefore, the standard error of the mean is $1.789 .$

The average distance between the sample means and the population mean in repeated sampling is roughly $1.789$.