 Hi Anthony. I'm looking at your homework in section 7.4 and let's look at a couple of these problems and I'm trying to figure out what you're doing wrong with Use of stat crunch on this first part the critical value The answer is 1.88 and you've got minus 2.69 to plus 2.69. Well, first of all This is just a one-tailed test not a two-tailed test So you wouldn't have two values for your critical value of Z and remember looking back up here Which you've got right the null and the alternative the alternative just has the greater than symbol Which tells you that's a one-tailed test and also that it's the right tail or upper tail test If this had been not equal Then you would have had a two-tailed test But it's it's not the alternative is a greater than which is a right-tailed test. So let's look at stat crunch You get stat crunch to come up here Okay, I had a problem there with my windows configuration for a second anyway, here's stat crunch and I've already Called up the normal calculator, which I think you know how to use just stat calculators normal get you this thing and We know it's a right-tailed test. So our symbol should be the greater than or equal and our alpha is 0.03 so we put 0.03 in the probability I'll just Click that out and Recalculate and so we get the critical value of Z is 1.88 just a single value I was trying to guess and The only way I could come close to what you had was by putting an extra zero in there and Then I get it two point seven four. I think your answer was 2.69 and it I don't know what you did to get two point six nine But again, the main thing this is just a right-tailed test With a critical value of 1.88 okay, let's look at the next part you picked the right pick Graph of the rejection region the upper tail test now the next thing is what is the standardized test statistic? And the answer is six point two eight and you had minus five point five two life Me I don't know how you come up with the minus If we call up the the Proportion Calculator I'm wondering let me just see if we go to Z stats one sample with summary if somehow you use this in order to come up with Your answer, I don't know if that's what you did but on proportions What you need to remember is that we always use the Proportion stats it is a Z test But we use proportion stats for proportions and we've got a one sample with summary That's what we come up here, and it's critical. It's very sensitive to Entering the data correctly We're we've given we're given the end of 1040 and the X bar The P hat I'm sorry that X bar P hat our sample proportion is point four And so you've got to multiply that out either in your calculator or you can you can do it in stead crutch We went to but it calculators probably faster and you get 416 successes out of that 10,000 I'm sorry 1040 observations and then setting up the hypothesis test for The proportion of point three one and remember it's a right tail test So it's very important that you select the right tail, and then we click on compute And we get our Z stat of six point two eight, which is what they came up with and our P Value is very very small, so we would we would reject The null on your answer over here You were consistent you said the Z Stat was minus, which is definitely not in the rejection region. Therefore, you would fail to reject and so I'll give you a Some credit for that and But in general I don't see what you're doing wrong here Going back to problem three You you made an error there on your critical values and again, you've got a two-tail test two values and Up here you've identified The alternative and the null correctly. This is a one-tail Lower-tail test so our critical value of Z is going to be a negative number But you won't have two values. You just have one and let's just Look at our calculator again here if we've got a one-tail test and it's a lower-tail test So I want to point it that way and alpha is 0.01 all of that's down there so The critical value of Z is minus two point three three and I'm wondering if you put in Half no, I don't know. Let me see. What is two point minus two point seven oh four what kind of Probability that's point. Oh, oh three. I I don't know where there where you're getting that For the life of me, but if you put in the one-tail lower-tail test put all alpha down there You will get the correct answer there so Let's look at one more Okay, here's problem five you got the null and the alternative stated correctly since the alternative is a not equal that makes it a two-tail test and so you would have a negative and a positive value of Z critical and You just put in just the negative the lower-tail. I don't Know why he did that, but if you use stent crunch you will get the correct answer Alpha is point oh eight so for a two-tail test you put alpha over two in each tail and so down the lower tail is point oh four and that gives a Stent or excuse me a critical value of Z on the Okay, Anthony had that phone call come in and let me get back on track this was a two-tail test and Since the alpha was point oh eight we put half of alpha in each tail the lower tail is A critical value of minus one point seven five and then we can do the upper tail of course point oh four and That's plus one point seven five so you've got two rejection areas zones with the area under the curve of point oh four and point oh four And again, I'm not sure how you got minus point two five But this is how you do it using stat crunch correctly the other part is the actual hypothesis test and you correctly selected the the sketch which showing the two tails the plus and minus and If you got two tails and you have to have a plus and minus critical value of Z if you've got one tail you have one Value of critical Z the test statistic we can calculate using a formula but of course where I recommend using the Stat crunch because this is another proportion Problem we use proportion stats one sample with summary It comes up and in this particular problem We don't have to do the little calculation there. It gives us number successes for one observations one thousand the Hypothesis is point four four and it's a two-tail a not equal and click on compute Let me get that out of the way so we can concentrate here a little bit Anyway, there's a summary of our test that matches the hypothesis that you you wrote down And our Z statistic is minus two point four eight Four and if you start rounding that you might get two point four nine, but let's just call it two point four eight You got minus two point five five. What I'm guessing there is that you entered some Value if you use the proportion test that you entered one of these values incorrectly But as I said earlier, you may have not thought to use the proportion Instead of the standard Z test And again because this is What was our critical value our critical value is plus or minus You did that again there point oh four so we can see our little test there The rejection regions is anything Smaller than minus one point seven five and of course minus two point four eight is out here Which is within the rejection region and also We get the same answer when we run our test We get a p-value of point oh One three which is less than our p or alpha of point oh eight therefore both those things tell us to reject the no So I hope this little review shows you How you can get the right answers using stat crunch and if it doesn't help you give me a holler