9.2.18Question Helpgample Oingalecuad Tom nnb DopulbbonR=59 and $ = 12, what is tha value of tSTAT #you Bra testing te null hypothesis Ho: {STAT (Type = Inecoucdeon...

The null hypothesis, $H_{o}: \mu=16,$ was tested against the alternative hypothesis, $H_{a}: \mu<16 .$ A sample of 50 resulted in a calculated $p$ -value of 0.017 . If $\bar{x}=14$, find the value of the population standard deviation.

We want to conduct the hypothesis test given using a classical and be the P value approach. We have H not H a N X and alpha. Listen at the top of the document. Yeah. Step 012 in the first part of three are identical for both tests. So we compute them simultaneously and then for the latter part of step three and then for step four, the approaches differ so we divide them at the bottom the document. So first check the requirements to be able to conduct this test, we see that mp times one minus P is equal to 37 which is greater than 10. So we're allowed to use the normal distribution Steps one and 2 are already complete as I've listed here hypotheses, an alpha level are already stated. The first part of step three is to calculate the testes cystic z. We find that p hat is X over and 78 over 154.52 So, plugging that with P and N into our Z. Z equals 2.738 Now, for the classical approach, we need to find the critical value associated with our outfit equals 0.1 From AZ. Table. This is negative 1.28. Since our Z score negative .738 is not less than our critical value. We conclude that P is not in the critical region and we fail to reject the null hypothesis. Next for the P value approach as the next part of step three, we simply have to calculate the probably the Z is less than R. Z score or 30.23 So we conclude that since P is greater than alpha, we failed to reject it.

We want to conduct the given hypothesis test using a a classical and be a P value approach step zero to the first part of step three are all the same for each test, so we complete them simultaneously. Then the second part of step three and step four are separate for classical and P value. Hence how we've separated amount of body this document. So to start off with we want to check the requirements to use the normal distribution for this population proportion test, N p times one minus P is 75 which is greater than 10. So it's appropriate to use the distribution. Steps one and two already complete the hypotheses and alpha are given the problem. For the first part of step three we calculate the testes, cystic C p hat is just X over N 4.24 and plugging into Z. We obtain the equals negative 0.46 Next proceeding first of the classical approach, we have to find the critical value for our alpha 0.1 from a Z table. We see that CC equals negative 1.28 which allows us to conclude P had is not in the critical reason. So do not reject a shot next for the P value message, we find the P value. That is the probability that Z is less than negative 0.46 Rz value. This gives a P value of 0.32 to eight from which we conclude P is greater than alpha. Do not reject H now.

This lesson in this lesson. We have that now how protesters us. The miracle to five. And alternate hypothesis sisters. The mean less than five dummies. We have a lower till test. And uh sample size it cost to 12. So the first one we are looking at P. For probability that tea with a degree of freedom of 11. Okay So T with a degree of freedom of 11. It's less than the test. Just. Okay so when we look for 2.05 yeah 2.05 is actually between 1.796 and 2.20 one. So that means this The people is between 0.05 and 0.2 0.025. Okay. It's a bit skewed toss the 2.201. So it means we can have around joe point 30 or something. Yeah so we have the P. Value which is between 0.05 and zero 0-5. Can have a p. value Which we change their own zero. Sorry. Very awesome. Let's look at the part where we have and they get to 1.84. Since we are deliver the lower time will still look at 1.84 and only getting 1.84. So 1.84 on this 1.8 for between these two values. So we still have 0.05 and there are points there too five. So you have 0.0 chief five game and Gerald point Gerald five. But this time it's cute On this side. So we can have their point there. Or four very close to this value then to that value A super. The last part where we have T. North which is called 0.4. So 0.4, 0.4 is between zero and 0.697. Okay so we have your .05. Between these two values. The one until they open five. And there are 125 By Skill does 0.25. So you have the p value of Jessica between zero coin 5. 225. Guys keep those are from two first. You can have a P value just around your 20.3 six And a third for something like that. Okay so thanks for time this is the end of the lesson.

So we're gonna look into different scenarios and create some hypotheses. So in no hypotheses and alternative. So the 1st 1 we're gonna look at is that a farmer claims that his chickens have a mean wait. So the mean of 56 so equals 56 ounces. So are no hypothesis or what the standard is without testing that knowing that information that we think it's gonna be different than that, Then we would see a Chavo, which just means the null when I should write that above just so we don't get confused later. So the no so h of oh, it's going to be are mean actually equals 56. So that would be the standard of what was the old data that we think so the mean is 56 ounces and then our alternative. So what will you be testing? The hunch that we have that something is different is age of eso alternative. The mule is going to be not equal to 56 so we think it is something different and that means that the mean is not 56 ounces. So then the next scenario that we're given IHS the mean of I think this is jets yet mean of jets? Um, age of jets is less than or less than sometimes people like me right out. So less, man. 18 years. So the standard or the null before we think that there's anything different is we would have our average or mule of 18. So equals 18 so the mean is actually 18 years. But again, we're testing because we don't think that that's true. So we want to see an alternative to that fact of mule is less than 18 years. So what is the possibility that it might not be that and it might be less than 18 years? Then we're gonna have our final one of our mean of our monthly credit card amount is more than $400. So again are no is gonna be the old data of we might have thought maybe it was the mean was $400. So, I mean is 400. But we have new data that maybe makes us think that that's different. So our alternative h of a is going to be. We think it might be more than so greater than 400. That's what we're testing for. So it would be the mean more than the $400. Thank you. So that's what we test there.