Question

He 99.7% confidence interval for the mean of a population is (14, 44). What is the value of s divided by square root of n

Answer 1

Range of population mean = Sample mean +/- Z*s/Sqrt (n)

If s/Sqrt (n) = x, then
(14,44) = sample mean +/- Z*x

At 99.7% confidence level, Z = 1.96
But
Sample mean = (min. range + max. range)/2 = (14+44)/2 = 29

Then,
14 = 29 -Z*x ---- (1)
44 = 29+Z*x ---- (2)

Applying any of the equations, say (1),
14 = 29 - 1.96*x
-15 = -1.96x
x = 7.653

Therefore,
x = s/Sqrt (n) = 7.653