Answer:
The mean is 2.75.
The margin of error is 0.62.
Step-by-step explanation:
In this case, we know the 95% confidence interval, and we want to know the mean and the margin of error.
The mean can be calculated as the average between the upper limit and lower limit:
[tex]\mu=\frac{UL-LL}{2}=\frac{3.37+2.13}{2}=\frac{5.5}{2}=2.75[/tex]
The margin of error is the difference between the upper (or lower limit) and the mean. It equals the product between the z-value and the standard deviation divided by the square of the sample size.
It can also be calculated as half the difference of the limits of the confidence interval.
We only have the limits of the confidence interval to calculate the margin of error:
[tex]ME=z\sigma/\sqrt{n}=\frac{UL-LL}{2}=\frac{3.37-2.13}{2}=\frac{1.24}{2}= 0.62[/tex]
