00:01
So in this question, first we need to define the distribution that we're going to use.
00:05
In this case, we are going to use the t -distribution indeed because here our sample size is smaller than 30.
00:14
Okay, then the point estimate for or the best estimate for the average in the population is the average in the sample, so it's indeed 5 .1.
00:25
The standard error here is given by the standard deviation in the, that they found in the sample, divided by the square root of the sample size, so this is 0 .35.
00:38
Then we need to find the critical values for this confidence interval, for the 95 % confidence interval.
00:45
So using the t -distribution, the two critical values, they are like here and here.
00:51
Because they're asking two, i'm gonna give two, but usually we use just the positive.
00:56
So in this case, because we want the 95%, this is the middle area that we have, which means that these two areas, they sum up to the 5%, so in this case 2 .5 % for each area.
01:08
And the degrees of freedom for this t -distribution is given by the sample size minus 1, so in this case 24.
01:15
So using the t -table, you're gonna get that this is 20639 and this is negative 20639.
01:24
So indeed, the two critical values are this, the negative, and the positive.
01:34
Then we find here the margin of error for the 95 % confidence interval.
01:40
So the margin of error for this confidence interval is given by the positive critical value times the standard error, which will give us the value 0 .7224...