Test the claim about the difference between two population...

Test the claim about the difference between two population means u1 and u2 at the level of significance . Assume the samples are random and independent, and the populations are normally distributed. Claim: u1 is less than or equal to u2; level of significance =.01. Assume o 2 over 1 does not equal 2 over 2. Sample statistics: x1=2416, s1=170,n1=12 and x2=2309, s2=51, n2=10 Identify the null and alternative hypotheses. Identify the standardized test statistic t Identify the p value Identify whether or not you reject or fail to reject the null.

Transcript

00:01 So in this question we're testing a claim about the difference of two population means at a certain level of significance.

00:08 So our claim is that mu1 is less than or equal to mu2 at a significance level of 0 .01.

00:21 So now we're meant to assume that sigma1 squared is not equal to sigma2 squared, and so that means that we're going to have to do welch's t test.

00:41 So our sample statistics are x1 bar is 2416, s1 is 170, and n1 is 12, whereas x2 bar is 2309, s2 is 51, and n2 is 10.

01:01 Our null hypothesis is going to be the strongest hypothesis which is not the claim, so that is going to be something like mu1 equals mu2, and our alternate hypothesis is going to be that mu1 is less than mu2.

01:20 So now we are going to identify the test statistic t, and t for welch's t test is x1 bar minus x2 bar divided by the square root s1 squared over n1 plus s2 squared over n2.

01:39 So let's calculate that.

01:44 2416 minus 2309 is 107.

01:49 Divide that by the square root of 170 squared over 12 plus 51 squared over 10, and we get a t of 2 .0714.

02:07 So that's our test statistic, but in order to calculate a p -value, we're going to have to get the degrees of freedom, and the degrees of freedom are given by the satterthwaite approximation as s1 squared over n1 plus s2 squared over n2 squared divided by s1 to the 4 over n1 squared n1 minus 1 plus s2 to the 4 divided by n2 squared n2 minus 1.

02:39 So the numerator is 170 squared over 12 plus 51 squared over 10 squared, which is 7120536 .454, and in the denominator we have 170 to the 4 divided by 12 squared times 11 plus 51 to the 4 divided by 10 squared times 9, and that gives me 534795 .9304...

Question

Please give Ace some feedback