Question

A teacher found that the mean number of pets, the students in her 5th grade class own, is 3 with a margin of error of 2.5. Construct a 95% confidence interval.

Answer 1

The margin of error is defined as
$E=z^{*} \frac{\sigma}{ \sqrt{n} }$
where
σ = population standard deviation
n = sample size
z* =  aconstant that depends on the confidence level. 
        At the 95% confidence level, z* = 1.96.

The confidence interval is calculated as
(μ - E, μ + E)

Given:
μ = 3, the mean number of pets,
E = 2.5, margin of error at the 95% confidence level.
Therefore the 95% confidence interval is
(3 - 2.5, 3 +2.5) = (0.5, 5.5)
Because we can only count whole numbers of pets, the confidence interval is (0, 5).

Answer:
At the 95% confidence level, the 5th graders own between 0  and 5 pets.