00:01
To construct a 95 % confidence interval to estimate the difference in population means, since we have the sample mean standard deviations and sample sizes, we're going to calculate the pooled standard deviation.
00:17
And that's the square root of the sample size minus one times the standard deviation squared plus the second sample size minus one times the standard deviation squared over the sum of the sample sizes minus two.
00:48
And so this is the square root of 18 minus one, so that'd be 17 times the standard deviation 8 .8 squared plus 19 minus one, which is 18 times the standard deviation of 9 .2 squared over 18 plus 19 minus two, which is 35.
01:20
All right, so the square root of 17 times 8 .8 squared plus 18 times 9 .2 squared over 35 is 9 .0079.
01:49
And then we'll calculate the standard error by the square root of the standard deviation of the first sample squared over its sample size plus the standard deviation of the second sample squared over its sample size.
02:11
That calculates to 2 .959.
02:33
And then we can calculate the margin of error using the critical t times the standard error.
02:45
The t is the critical value corresponding to a 95 % confidence level and 35 degrees of freedom.
02:55
And that's 2 .032 times our 2 .959 standard error and the margin of error.
03:05
I'm going to go four decimal places...