The margin of error is defined as
[tex]E=z^{*} \frac{\sigma}{ \sqrt{n} } [/tex]
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.
