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

In this video we’ll see how to assess the Z-teststatistic and p-value for the two percentage Z-test. The recommendations for theTI-83 and eighty four are identical. And we are going to start with this instance, the identical one we used for thetwo share Z-interval. Simply to summarize the trouble,we have a current provider and now we have a prospective provider. And we need to comprehend is there proof that the potential provider has a larger price of passing the inspection when you consider that in the event that they do we’regoing to head with them. So our null speculation isthat the genuine proportions that might move inspection arethe identical for the two corporations and our alternate hypothesis, the one we’re looking to seeif there’s proof for, is that the prospectivesupplier has a greater expense of passing inspectionthan the current supplier. So, first we stock out the preliminary steps. We set our value stage alpha, we need to anticipate that there is two unbiased,random samples right here.And now, one-of-a-kind from when we did the two proportionZ-interval, we’ll appear at this variety, which isthe pooled percentage, p-hat. And the rationale for this isbecause now we have a null declare that says that the p1 equals p2. So in a similar fashion to after we didthe one percentage Z-experiment and we had a hypothesized worth for p, we use that hypothesized valuein checking our stipulations and in calculating the SE. So here what we’re going todo is use our great estimate for what this proportion thatthese two equal possibly. And so our great estimate for that’s to combine our two sample proportions. And we try this through addingthe complete number of yeses over the whole sample dimension and right here we get zero.9285. So this range we’ll use when we investigate our conditionsand we’re additionally going to use it within the SE system.So here we now have ourn1[p-hat], n1[1 minus p-hat] n2[p-hat] and n2[1 minus p-hat] are all higher than or equal to 10. And now after we calculate our SE, we ought to go to the formula sheet and we’re looking at thedifference of sample proportions and we’ve this specialcase the place p1 equals p2. That is our null hypothesis. So on the grounds that we’ve got this hypothesis here, we’re going to use thisstructure written here for our SE. So we have p-hat right here, 1minus p-hat, et cetera.So we fill in the numbers, and now we’re equipped tograb the calculator. So, we invariably with STAT, exams, 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’s. So x1 is 899, n1 is thesample measurement of 1000, x2 is 958, bear in mind x1 andx2 need to be integers. Of course, n1 and n2 haveto be integers as well. So n2 is also one thousand. And now our alternate claimis that p1 is lower than p2, so we’ll decide upon the less than and now we will do Calculate. And we see we get a Z-rating of -5.12 and a p-worth very, very small. Notice this also gives youp-hat, the pooled proportion. So this is our .9285, whichis what we calculated right here and they healthy. So what’s our conclusion? Our p-value is way less than alpha, so we reject H sub zero,we now have proof that the prospective provider hasa larger proper go inspection than the present provider, so we should go along with theprospective provider.That’s it for this video, in case you appreciated it supply it athumbs up and subscribe below. Thanks for gazing.. 