# 2-Proportion Z-Test (Hypothesis Testing) (TI-83 & TI-84)

In this video we are going to see how to evaluate the Z-teststatistic and p-value for the 2 share Z-experiment. The guidelines for theTI-eighty three and 84 are equal. And we’ll with this instance, the equal one we used for thetwo percentage Z-interval. Just to summarize the concern,we’ve a present supplier and we now have a potential supplier. And we wish to comprehend is there evidence that the potential supplier has a better expense of passing the inspection due to the fact that in the event that they will we’regoing to move with them. So our null speculation isthat the true proportions that may go inspection arethe identical for the 2 organizations and our alternate speculation, the one we’re trying to seeif there’s proof for, is that the prospectivesupplier has a bigger fee of passing inspectionthan the current supplier.So, first we feature out the initial steps. We set our importance level alpha, we have to expect that there’s two unbiased,random samples here. And now, exceptional from once we did the 2 proportionZ-interval, we’re going to seem at this quantity, which isthe pooled percentage, p-hat. And the motive for this isbecause now we have a null declare that says that the p1 equals p2. So in a similar fashion to when we didthe one percentage Z-test and we had a hypothesized price for p, we use that hypothesized valuein checking our stipulations and in calculating the SE. So right here what we’re going todo is use our pleasant estimate for what this proportion thatthese two equal perhaps. And so our best estimate for that’s to mix our two sample proportions. And we try this via addingthe complete number of yeses over the whole sample size and here we get 0.9285. So this number we will use once we check our conditionsand we’re additionally going to use it within the SE method.So here we have ourn1[p-hat], n1[1 minus p-hat] n2[p-hat] and n2[1 minus p-hat] are all bigger than or equal to 10. And now after we calculate our SE, we must go to the formulation sheet and we’re watching at thedifference of pattern proportions and we have now this specialcase the place p1 equals p2. This is our null hypothesis. So due to the fact that we have now this hypothesis right here, we’ll use thisstructure written right here for our SE. So we have now p-hat here, 1minus p-hat, et cetera. So we fill within the numbers, and now we’re ready tograb the calculator. So, we at all times with STAT, tests, and this time we’re goingto go to 2-PropZTest. So let’s go to STAT, assessments,and to find 2-PropZTest. 2-PropZTest, here it is. So x1 is 899, n1 is thesample dimension of one thousand, x2 is 958, take into account x1 andx2 have got to be integers.Of direction, n1 and n2 haveto be integers as well. So n2 can be one thousand. And now our alternate claimis that p1 is lower than p2, so we’ll select the less than and now we will do Calculate. And we see we get a Z-score of -5.12 and a p-worth very, very small. Detect this additionally offers youp-hat, the pooled proportion. So this is our .9285, whichis what we calculated here and so they in shape. So what’s our conclusion? Our p-worth is far not up to alpha, so we reject H sub zero,we now have evidence that the prospective supplier hasa higher proper go inspection than the present provider, so we will have to go with theprospective provider.That is it for this video, should you appreciated it supply it athumbs up and subscribe beneath. Thanks for observing..