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Identify the degree of confidence when the area in each tail is .05.Select one- 909b. 95%989d. 99%...

Question

Identify the degree of confidence when the area in each tail is .05.Select one- 909b. 95%989d. 99%

Identify the degree of confidence when the area in each tail is .05. Select one- 909 b. 95% 989 d. 99%



Answers

Find $\alpha,$ the area of one tail, and the confidence coefficients of $z$ that are used with each of the following levels of confidence. a. $1-\alpha=0.90$ b. $1-\alpha=0.95$
c. $1-\alpha=0.99$

We want to find the critical T. Value TC. Such as the following conditions are met when constructing a confidence interval about a population, meaning you remember whenever finding A. T. C. Value that you're going to make use of a tea table tables can be found on google and textbook and a map right tail areas for corresponding degrees of freedom onto the associated TC. Value for the students to distribution. So to start off with for part A. For retail area 0.2 degree freedom 19 Using a tea table, we see this maps to T. C. Equals 2.205 part B. We have a near identical problem with retail area 0.1 degree of freedom 32 giving us T equals 1.309 for part C. We want to find the left tail area 0.5 with degree of freedom six. To find a left tail area from the tea table. We simply have to note that students distributions are symmetric about their mean zero and what's to the right of a positive T. Scores the same which was still left of a negative to score. So taking the negative all right tail area for these conditions 00.5 degree Freedom six. We obtain T equals negative 1.943 Finally, for part D, does offer to tail area. We simply note that the right tail area is equal to half of the retail area. In this case 0.25 we identify that area corresponding to the same degree of freedom 16 to obtain T. Value Plus or -2.12.

We want to find critical T. Score TC. Such the following conditions are met to identify any such TC score. We're gonna start by noting that we're going to make use of a T. Score table which for a particular right tail area and the degree of freedom allows us to match that area onto the corresponding TC value. So for instance right and tail area 0.1 degree of freedom 25. Using the tea table. Either on google or in a textbook, we obtain T equals 1.316 for part B. We have an identical problem with right tail area in the specified degree of freedom, which gives us T equals 1.697 Next to find the left tail areas to the part C. We have to identify the fact that we're gonna use symmetry to solve this problem, that is the area to the right of a positive T. Score is the same as the area to the left of the negative T score because of the symmetry of the student's T distribution using symmetry and finding the negative right tail area gives us T equals negative 2.55 to finally, for part D. To identify a to tail area T. Score, we simply divide our to tail area by two and find the right tail area corresponding. So in this case that's a retail area of 20.5 point one degree of freedom 20. That gives us a T value of plus or minus 1.725

In this exercise, we are asked to find the t percentile required to construct various one sided confidence intervals. Now remember for a one sided confidence interval for a given confidence level they needed to percentile is the percentile that has an area of alpha in the tail. And it's from the distribution with k degrees of freedom. So for part A we're asked to find the t percent. L. For a one sided confidence interval When the confidence level is 95 and the degrees of freedom is 14 means that we want the following per cento. So we can look this up in any T table or use software, We want an area of .05 in a single tail And the degrees of freedom is 14, so we get 1.761. Now for part B were given a confidence level of 99 and degrees of freedom of 19, which means that we're looking for the following percentile and then going back to the table An area of .01 in that upper tail. And we have 19° of freedom. So our percentile is 2.539. And for part c the confidence level is 99.9%. And the decrees of freedom is 24 and back to the table. So my table does not have Call them 4.001 in a single tail. So instead I used software to find this value And it comes out to three 467

This is ST T distribution and recall this off value here, the area to the right off this see value and this offer value here is the area to the left off the T value here. Now let's see value here is that see value for the upper till area. This is the opportunity area. Let's see value here is that see value for the lower tail area and this is the lower tail area. The Twitter area under this graph this one and from this point, the area from the right side or the area to the right side of you. It's 0.5 and the area to the left side of his you it's 0.5. So when you add this and that gets one all sorts of symmetry for the TD specially have this relationship. I have this and in that it is equal to the negative off this note that the V s degrees of freedom and it's the same here, or I can restate this relationship us that essentially I'm want supplied the first question by negative. And so I obtained this second question. Now let's solve the question. We are finding the t value for a number of cases. For parts E, you have an area off. Zero point is you one that is the opportunity area with a degree of freedom off 10. Now from the diagram usually own the opportunity areas dish, it'd portion and the T value looking for us, this area so and noticed as the trigger for them. He is d f but in the DAG and we used to be so the next you're going to do is going to read this value from the TT situation table from the table. I obtained this value. This, then, is the upper till the T value for the opportunity area off 0.1 for Parts B. I have a lower till area off 0.5 with a degree of freedom off 20. Let us not forget that we are finding the T value associated with this Louisville area from that city's tuition table or from the diagram. This is the Louisville area, and this is the T distribution or the T value we are looking for, and it is negative. So going to read the positive vision off this from the T distribution and then when they get whatever we obtain. So there's the value obtained from the distribution table. Now, when we negate it, the value you obtained will be the results. We are looking for Parts B. Therefore, this is the T value. Associate it with a part B for part C. We are finding to t values such that the area between them isn 85% was your prints 95 So I'm going to use the diagram to answer this question. There's your acquaintance year and then to the right off the zero value the areas is your 0.5 and then to the left off the duty value. The area is your 0.5 because the value I'm looking for the area looking for its native 5% or your points 95 It means part of it is on the left off zero and then parties is on the right of you. So if I represent the T value to the right off zero s key and the T value to the left of us, negative key, then let me indicate the area here. The area between them is 0.95 Therefore, to the rights off negative key. The air a softened into the left off. Positive, killed. The area is Alfa. Now we know that's the tutor area above or the to terry unreality value distribution. It's one. So when I some the areas the issued adept one. So I have to offer. Plus is your 0.95 and X equal to one, then are playing or Jibril Here I end up with one money is your points 9 5/2 and the value from the Kark leader is your points is you 25 So I'm going to look up this value from the tea distribution table. Remember, the question gives us a degree of freedom and that is 15. So from the tea distribution table, I get the value off 2.131 Now I'm going to get this to find the negative key value, and that is negative. Two points. One stir one. Therefore, between these two values, the area is 95% or 0.95 Now to question Pat's D pasties similar to Part C and the area is 80% was your points. Each time we use a diagram, two demonstrates or to answer this question just as I did for parts for patsy area to the right of zero is 0.5 and the average the left was U is 0.5. Because I'm looking for zero point eat pad off. It will be to the writers you and then powerfully to be to the left of you. So they see value to the left of you. I call it's negative key. And then to the right of you is key. And there let me indicate there area between these two points Suit my left. I have often into my right. I have Alfa When I some them issued out of toe one. Well, when I some them I have one so I'm going to sum them and then I have to off applies you point Age is a quote one and then I playing orgy right here Our Facey quote zero points one. I'm going to look up this area from the sea distribution table. The degrees of freedom from the question is 24 So from the tea distribution to have 10 1.318 I'm going to find a negative off this value so that is native 1.318 So these two values are. They see values we have to provide for parts D. Now for parts e the area between the two c values it's 99% or 0.99 I'm going to use a diagram to answer this just as I use for party the area to the right off zu 0.5 and then the area to the left off zoo. It's 0.5 I'm because I'm looking for the area off with your points 99 para free to be to the left off zero and then part will be to the right of you. So I indicate the area here and then I know that the area to my left is how far and then the area to my right is Alfa and when I some the serious I should have one. So I have to offer plus your points +99 year and that is equal to one. Using algebra, I obtained one minus 0.99 of a to and then the value using a car Kalitta is zero point Suz you're five So I'm going to find this cereal from the distribution table. The degrees of freedom from the question is 19 they're from the table. I obtained the value of 2.861 Then we will find a negative off this value, and that is negative 2.861 So these two values at it see values you have to provide for the question.


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