00:01
Hello everyone we are going to solve a question in this question we are given the data for two samples one is for quarters which is given as n1 is equals to 50 x1 bar is equals to one 5 .2 and s1 is equal to 10 .2 and the second is pan is for this n2 is equals to 60 x2 bar is equals to 1 1 .2 and s 2 2 is equals to 12 .3.
00:33
Now in this we have to write the hypothesis and to conduct the test.
00:39
So here we assume that mu 1 is equals to actual mean, actual mean age of, actual mean, actual mean age of all quarters, all quarters in circulation, in circulation.
00:56
And here we assume that mu 2 is actual mean, actual mean h of all pan is, all pan is in circulation.
01:12
So, we write the hypothesis.
01:16
The null hypothesis that is h0 is given by mu 1 equal to mu 2 and the alternative hypothesis that is h1 is equals to mu 1 not equals to mu 2.
01:26
Sorry here we have mu 1 greater than mu 2 and here alpha is given as 0 .05 so firstly we find the test statistic value that is t is equals to x1 bar minus x2 bar divided by here we have sp under root here we have 1 divided by n1 plus 1 divided by n 2 and this sp is equal to s p is equal to under root n1 minus 1 s 1 square plus n 2 minus 1 s 2 square and divided by n 1 plus n 2 minus 2 here this is defined as sp now when we solve this we have s p is equal to firstly we find the value for sp on putting all the values sp comes out to be under root 1 to 9 .8 which is equals to 1 .395.
02:29
And when we put the value in t, so this t comes out to be 15 .2 minus 11 .3 .95.
02:39
And this multiplied with under root 1 divided by 50 plus 1 divided by 60.
02:46
This is here we have 1 divided by 50.
02:50
And on solving this comes out to be 1 .8332...