00:01
Here we have to obtain the confidence interval for the means of the difference of the two populations.
00:05
So, the first population, the summary statistics given are n1 equal to 11, n2 is equal to 13 and sample average x1 bar is equal to 131, wherein the second population it is 162 and the sample standard deviation for the first population is 30, whereas for the second population it is 30 and we have to find the confidence in 95 percentage confidence interval is needed.
00:32
So, alpha is 0 .05.
00:34
First we can consider or take find the values of the terms x1 bar minus x2 bar which is 131 minus 162 which is obtained as minus 31.
00:45
Now we can obtain the standard error of x1 bar minus x2 bar which is given by the formula co -root of n1 minus 1 into s1 square plus n2 minus 1 into s2 square divided by n1 plus n2 minus 2 into 1 by n1 plus 1 by n2.
01:08
On substitution the corresponding values and on simplification the standard error is obtained as 12 .9750.
01:17
Here the critical value used can be is using the t tables with degrees of freedom n1 plus n2 minus 2 and this we can write as alpha is 0 .05 by 2 and the degrees of freedom n1 and n2 are 11 plus 13 minus 2.
01:35
Using excel function we can find this critical value t dot inverse dot 2t since it is a total t value needed then the level of significance alpha and the corresponding degrees of freedom we can just substitute and the answer is obtained here...