00:01
Hey there, welcome to numerate.
00:03
So we are looking at their fluency test scores of eight subjects here.
00:09
So we are asked to, at the end, constructing 95 % confidence interval.
00:15
So therefore, we would have to find the components of that first.
00:19
So starting with part a here, part a, what is the point estimate of the population mean? so the point estimate will be just basically the sample mean.
00:32
So we're going to take the sum of x divided by our sample size 8.
00:39
This will give us a mean of around 8 .875.
00:52
Part b, what is the standard deviation of the sample? the standard deviation will be the sample standard deviation, so the s equals the square root of, the sum of squares, so sum of x minus the mean of 8 .0 .9 squared, care of the digits, remember when calculating, divided by the sample size minus 1.
01:26
So what we have here is 8 minus 1.
01:35
This gives us a standard deviation of around 2 .900.
01:54
All right, perfect.
01:58
Now we are asked for part c, what is the estimated standard error of the sample mean? so see, the standard error equation is basically the standard deviation s divided by the square root of our sample size.
02:16
So we have a standard deviation of 2 .9 divided by the sample size of eight individuals.
02:26
Therefore, we're going to compute this and see what we get.
02:31
So we have our standard deviation as 2 .9 divided by the square root of 8, our sample size.
02:42
So let's see what we get.
02:44
We get a value of 1 .025...