00:01
Hey there, welcome to newmary.
00:02
So we're trying to find the minimum sample size, right? so how many students must be randomly selected to get a mean of weekly earnings of students at a college? so we want a 95 % conference interval with the sample mean and sample mean is within four of the population mean and the population standard deviation is known as 53.
00:28
So with that, we're going to set our, margin of error equation because we see within 4 that means the margin of error so margin of error equals we have a population standard deviation so we're going to do z -distribution so z -critical multiply 2 so standard population standard deviation denote as sigma divide by a square root of n so we're trying to find the square root of n over here so what we're going to do now, we can plug in our values here, so we get a margin of error is within 4.
01:10
Lz critical with the 0 .95 confidence level will be 1 .96, multiplied by the population standard deviation, which is known to be 53, divided by the square root of n, which we're trying to find.
01:28
All right.
01:31
Okay, so we have that.
01:33
Now let's move the variables around.
01:36
So we're basically going to have, let's see.
01:42
So we have, let's move to 1 .96 to the other side first.
01:45
So divide by 1 .96...