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.

Short answer

The standard error of the mean is $1.789$.

Step-by-step solution

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.

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 $1.789$.