00:01
So to find the 95 % confidence interval for the difference between the two population means, when the population variances are not assumed to be equal, you can use the two sample t distribution.
00:14
So the formula for the confidence interval is equals x1 minus x2 plus or minus t alpha over 2 times the square root of s1 squared over n1 plus s2 squared over n2.
01:00
Where x1 and x2 are the sample means of the two groups, s1 squared and s2 squared are the sample variances of the two groups.
01:13
N1 and n2 are the sample sizes of the two groups.
01:16
T alpha over 2 is the critical value for the t distribution for a 95 % confidence interval with the appropriate degrees of freedom.
01:24
So for the first sample, x1 equals 50 .2, s1 squared is 4 .4, n1 equals 12, and for the second sample, x2 equals 47 .8, s2 squared equals 6 .3, and n2 equals 15.
01:43
So we first need to get the degrees of freedom for each sample.
01:57
So for a two sample t -test with unequal variances, you can use the formula for degrees of freedom, where degrees of freedom equals s1 squared over n1 plus s2 squared over n2 squared divided by s1 squared over n1 over n1 minus 1 plus s2 squared over n2...