00:01
In your question, we're told to find the critical value that should be used for a 90 % confidence interval, and the sample size is 44, and then they give us the sample standard deviation and say that the population standard deviation is unknown, and the population itself appears to be skewed, not normally distributed.
00:25
They're trying to trick you into possibly using a t critical value.
00:29
However, the central limit theorem states that if our sample size is larger than 30, so this is greater than 30, the sampling distribution of the sample mean will be approximately normal.
00:48
So it's okay for us to use a z critical value here, even though the population standard deviation was unknown and it was possibly skewed.
00:59
The central limit theorem kicks in for this large sample size.
01:04
All right, so what we're going to do to find that z critical value is we're going to sketch this.
01:12
The z critical value is the z score at the upper boundary of the middle 90 % since it's our confidence interval.
01:21
We have to include the left tail in our calculation whether we use technology or a z table.
01:28
There is a total of 100%, but 10 % would be left to be split between the two tails equally.
01:37
So we divide this by 2, giving us 5%.
01:42
I'll put that over here and combine it with the 90...