00:01
In this question, we have to test the hypothesis based on the given information.
00:04
So, the value of delta not is here going to be zero.
00:08
Now, the value of x1 bar that is sample mean of the first sample is 6 .1.
00:14
The value of x2 bar is here going to be 6 .4.
00:18
And now the value of s1 that is standard deviation for the first sample as 0 .5.
00:24
Now, the value of s2 will be here equals to 0 .9.
00:28
And hence, we can say that the value of n1 that is sample size for this first sample is 37.
00:35
And the value of n2 will be here 47.
00:38
Now, the alpha value is here 0 .05.
00:42
Hence, we can say that null hypothesis would be here, let us write it is mu1 equals to mu2.
00:49
Or it can be here written that it will be alternate hypothesis, which is going to be mu1 minus mu2.
00:58
And then it will be here less than 0.
01:01
So, here the value of pooled variance is going to be equals to let us write, it will be here n1 minus 1 multiplied with it is here s1 square.
01:12
And then here it is n2 minus 1 multiplied with it will be here s2 raised to the power 2 divided by it is here going to be n1 plus n2 and then here it is minus 2.
01:26
So, this very value is here going to come around, let us write, it will be here sp square and then here it is going to be equals to.
01:35
So, if we plug in the value as we have written above, it will be here coming around 0 .7511.
01:42
And hence, we can say that the value of test statistic can be obtained from the formula, which is t0 and that is here x1 bar minus it will be here x2 bar minus delta 0 value...