type the correct answer in the box. helen gathered data on the fuel efficiency of compact sedans. her sample…
type the correct answer in the box. helen gathered data on the fuel efficiency of compact sedans. her sample contains 80 data points, and the standard error of the mean is approximately 0.595. what is the standard deviation? round your answer to the nearest hundredth. the standard deviation is approximately
Answer
Answer:
5.32
Explanation:
Step1: Recall the formula
The formula for the standard error of the mean ($SE$) is $SE=\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the standard - deviation and $n$ is the sample size.
Step2: Rearrange the formula
We can rearrange the formula to solve for $\sigma$: $\sigma = SE\times\sqrt{n}$.
Step3: Substitute the given values
Given that $n = 80$ and $SE=0.595$. First, calculate $\sqrt{n}=\sqrt{80}\approx8.944$. Then, $\sigma=0.595\times8.944$.
Step4: Calculate the result
$0.595\times8.944 = 5.31168\approx5.32$.