among 320 randomly selected airline travelers, the mean number of hours spent travelling per year is 24…
among 320 randomly selected airline travelers, the mean number of hours spent travelling per year is 24 hours and the standard deviation is 2.9. what is the margin of error, assuming a 90% confidence level? round your answer to the nearest tenth.
Answer
Answer:
0.3
Explanation:
Step1: Identify the formula
The formula for margin of error $E = z^\frac{s}{\sqrt{n}}$, where $z^$ is the z - score, $s$ is the standard deviation and $n$ is the sample size.
Step2: Identify the values
We have $n = 320$, $s=2.9$, and for a 90% confidence level, $z^* = 1.645$.
Step3: Calculate the margin of error
$E=1.645\times\frac{2.9}{\sqrt{320}}$ First, calculate $\sqrt{320}\approx17.89$. Then, $\frac{2.9}{17.89}\approx0.162$. Finally, $E = 1.645\times0.162\approx0.3$.