 Eileen, on this problem, 8.4.3, it's a problem about population proportions, and it's a difference of proportions, and we're given the alpha, of course, alpha in this case is 0.1. Confidence level will be 90%. We're given a claim that proportion one is not equal to proportion two, and that is a critical thing that you've got to read for, you've got to understand what is the claim, in this case they make it easy for you. The claim, because it contains a not equal, an inequality, in other words, it could be a not equal, a less than operator, a greater than operator, but it says the claim is not equal. Okay, Eileen, I'm back, I had a disruption there. I think I was saying that because the claim is clearly specified here that proportion one is not equal to proportion two, that tells you that the null is not the claim, and the null has to be the complement of this. The complement of not equal is equal. The next question, is this a right tail, left tail, or two tail? Well, anytime you've got not equal as the alternative, it's a two tail test, which means alpha goes on each side. I don't know if you ran this or not, let's just go ahead, I'm going to go to question, stat crunch, okay, we have a hypothesis test on a different proportions. Anytime we're working with proportions, we always use a z, I'm going to go to stat, z stat, whoops, two sample, I'm sorry, proportion stats, two sample and stat crunch, we use proportion stats, and we have a summary, I'm going to go up here, in sample one, we've got 27 for a number of successes, observations is 75, in number two, we've got 45 successes, observation 62, our hypothesis test is already pretty well set up, portion one minus proportion two is equal to zero, and the alternative is not equal to zero. So we're going to go ahead and hit compute, and we get this result there, we get a z stat, which we didn't check the critical value of z, I can show you that, but what we do know is our p value is very, very small, it's much less than our alpha of point zero one, therefore we reject the null hypothesis, let me drag this out of the way. So our options are, it says, should we reject the null, yes, we reject the null, and you had answered there is insufficient evidence to support the claim, well if the null had been the claim, you might have been able to say that, that's technically not the right way to say that, we always say we, you know, if there's insufficient evidence, it's failed to reject the null, but in this case, there was sufficient evidence, we reject the null, and since the alternative is the claim, there is sufficient evidence to support the claim. I know in this next problem, I'm not going to solve the whole thing for you, but I want you to listen to me here, again, it's a difference between two population proportions, and it tells us the claim, population one is greater than or equal population two, all right, so if you've got any equality, which this is, remember an equality is an equal sign, a less than or equal operator, or a greater than or equal operator, so since this is an equality, this is the null hypothesis, and therefore the claim is the null hypothesis. The alternative has to be the complement of this null, and the complement is P1 is less than P2, so it would have a less than operator which points to the left, and that should be your clue that this is a left tail test, remember it's always the direction that the operator and the alternative points that tells you whether it's a left tail or right tail test, or a two tail, again the two tail being if you've got an inequality not equal between and the alternative, and you got the right answer, fail to reject, there's insufficient evidence to reject the claim, in this case because the claim is the null, if we fail to reject the null, there's insufficient evidence to reject the claim in support of P1 is less than P2, so let's go on here and look at number four, and you got this one right, so let's don't take any time on that one, let's go to number five, you at part of it right, let's see you specified the correct null and alternative, you found the correct Z critical, or Z sub zero as I say, you said the rejection region would be any Z greater than that critical value of Z 2.33, you found the test statistic minus 496, you chose the correct answer, fail to reject the null, so what did you get wrong, at the 1% significance level which was alpha there is sufficient evidence to reject the claim, okay let's go back, we said fail to reject the null, what was the claim, the claim is the proportion of the adults who are smokers in the state is greater than, greater than is a operator that points to the right, so that means the is an inequality I should say, therefore the claim is the alternative, if we fail to reject the null that means there is insufficient evidence to support the claim, you said there is sufficient evidence to reject the claim, we said that there's insufficient evidence to reject the null which means there's insufficient evidence to support the claim, it's difficult sometimes in these word problems but make sure you understand what is the claim and what is the null and the alternative, if the claim is the null and you fail to reject it that means there is insufficient evidence, I'm sorry, if the claim is the alternative and you reject the null that means there is insufficient evidence to support the claim, let's go to the next one, okay you got almost all of this right and you're down here at the same conclusion again, let's go up here and look, you got the correct statement of the hypothesis, the null is less than or equal and the alternative is greater than which means it's a right to test, let's see, identify the claim and in the write up it says, can you support the claim that the proportion of 12th grade males who said they had smoked in the last 30 days is greater than the proportion of 12th grade females, so you've got that greater than, the greater than of males, the portion is greater than the portion of females, that's the alternative, that's the claim and the null is the complement, so down here our answer was we reject the null, you got that right, so if you reject the null that means you support the claim since the claim is the alternative, so we would say at the 10% significance level there is sufficient evidence to support the claim, again the alternative was the claim, the alternative always contains the inequality, in this case the claim was an inequality greater than and since we reject the null that means we support the claim, let's look at the last one, wow and this one, let's see what you got, .039, .081, I want to pause here for a minute, okay I laid on this last one, I took a few minutes just to look at it to see what you did and you missed it, this is finding a confidence interval for a difference in a proportion or two proportions and they give you the survey of a million 68,000 students of which 8.6, so they were planning studying engineering, here's another survey of 1.476 million students taking the SAT and they said 9.2% we're going to study engineering and we need a 90% confidence interval for the difference between the two proportions, they give you this long equation which you can plug into your calculator or Excel but we can do it using stat crutch, I'm going to bring this up and what I did here is just save a little time, I label these first two columns in for the number of, in each sample 1,068,000 and 1.476 million, we had 8.6% successes in the first sample and 9.2% successes in the second sample, if you go to the proportion to sample with summary that I showed you before you've got to have successes in observation not percentages in order to do this, so what you can do it very easily with just a calculator on your phone multiply the point or the 8.6% times that to get the number of successes in the first sample and multiply that again to get the number of successes in the second sample and again you can do that on your calculator on your phone for that matter, once you get that data all you got to do is put it in 91848106800, number of successes in the second one was 1.35792 and 1.476000, we want the confidence interval for the difference remember always to set that to be what you want, don't do like I do sometimes and leave it said in the default to 0.95 click on compute and we get this answer a lot of data there but what you're really interested in the lower limit is minus 0.006, so it rounds to 0.00, minus 0.007 which is that answer and the upper limit is minus 0.0005 and that still rounds to 0.005, so that's how you do that one, so I hope that helps