A confidence interval for the population mean computed from

A confidence interval for the population mean computed from an N of 16

ranges from 12 to 28. A new sample of 36 observations is going to be taken.

You can

Solution

estimated mean is midpoint of interval, i.e. 20.
margin of error for sample of 16 z x s/sqrt(16)=(z/4)s =8, assuming you use the normal dist z (using the t dist
for small samples is more appropriate, but complicates things since the problem didn\'t give the level of confidence, which would change the t-value for different degrees of freedom).
for a new sample of 36, the moe would be z s/sqrt(36) =(z/6) s.
So the moe for the new sample is 4/6 smaller than for a sample of 16, so it would be (4/6)8=5.33,
which gives from 14.67 to 25.33.