Question

A random sample of 500 army recruits has a mean height of 68 inches with

a standard deviation of 2.5 inches. If a 95% confidence interval is
constructed, with all the conditions having been met, what is the margin of
error?
O 0.22
6.02
184
68

Answer 1

The margin of error is 0.22

Explanation:

Mathematically, the margin of error at the given confidence interval can be calculated using the formula below;

Margin of error =
`t_(0.05/2)` × s/√n

where is the t-value at the given confidence interval, s is the standard deviation and n is the sample size

`t_(0.05/2)` = 1.96 (From t-distribution table)

s = 2.5 inches

n = 500

MOE = 1.96 × 2.5/
`√(500)`

MOE = 1.96 × 2.5/22.36

MOE = 0.22