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A group of IQ grade sludents Jfe sckcted and thcn numbered from U0 t0 99 Thc students are divided Into groups in the following manner: (00-05. 10-19. 20-29. ctc . s...

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A group of IQ grade sludents Jfe sckcted and thcn numbered from U0 t0 99 Thc students are divided Into groups in the following manner: (00-05. 10-19. 20-29. ctc . sample of ten of the students are chosen; which results mn the followIng students beinp selected:Four data gement students Trgucd about whrh sampling mcthod wcre used They suggested the smple could 6e example of multi-stage Tundom sumpling. stratified random sampling: cluster random sampling or sstematic randlom samplingWhich sampling

A group of IQ grade sludents Jfe sckcted and thcn numbered from U0 t0 99 Thc students are divided Into groups in the following manner: (00-05. 10-19. 20-29. ctc . sample of ten of the students are chosen; which results mn the followIng students beinp selected: Four data gement students Trgucd about whrh sampling mcthod wcre used They suggested the smple could 6e example of multi-stage Tundom sumpling. stratified random sampling: cluster random sampling or sstematic randlom sampling Which sampling Iacthod thc Icast Jikely to have been uscd? Justily sour Answer , Which enmpling uacthod Ile ntost Iikeby Io hve bcen uscd" Justily Yulii MisW ct; Be Sute lo dscut? why 1 more Iikely than Ihc rcnLuining (WO mcthods



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The IQ scores of ten students randomly selected from an elementary school for academically gifted students are given. $$ \begin{array}{lllll} 133 & 140 & 152 & 142 & 137 \\ 145 & 160 & 138 & 133 & 138 \end{array} $$ Grouping the measures by their common hundreds and tens digits, construct a stem and leaf diagram, a frequency histogram, and a relative frequency histogram.

So the problem gives us that the mean of it was equal to 108.9. The standard deviation of 13.17 the mean of G P A is equal to 7.447 a standard deviation of 2.1. Now, given the correlation is 0.6337 So first we need to find the least squares regression line for predicting GP A Given I keel, the key phrases least squares regression line. This tells us it's going to be a y equals MX plus being now we need to find em and be These are the two equations you should have written down for this. So I am or slow is equal to correlation time standard deviation y over standard deviation of acts and be our interceptor is equal to the mean of y minus slow times the mean of backs. So let's start with finding the swell first. So we have our that's 0.6337 and we have the standard deviation of y and x school were given in the problem which one was wide and which one was acts but you and if we didn't know that we can tell like you is going to be ex, cause that's the given and the one we're trying to solve for his g p A. So that's gonna be the why. So the standard deviation for G p A. Will go on top. That's the two point wine when a bottom will be the 13.1 Savannah and this is 0.101 now for B. We'll take the lean of why so 7.447 My minus the slow, which we just found is point y know, wine times the mean of X which is 108.9 and this is equal to negative three point by by 19 So now we can make our equation. Why is equal to em? So 0.101 packs minus three point by 519 and that is the end of part A. Now, for part B, we're going to calculates r squared. All we have to do is this. Take are from square it R squared is equal to 2.6337 squared, which is point for 016 Normally, you want this written as a percentage so 40.16% now for parts CIA. So a student has an I Q of 100 free and a G p a of 1000.5 free buying the residue on. Explain what it means. This is something else. You should have written down. Residue. U'll is equal to observe minus expected A. So we have our observed value. That's the 0.5 free. We're gonna be looking at the Wye Valley use of the GPS values. So we have a 0.5 free. We just need to find the expected. And the way we'll get are expected. It is by plugging in this 100 free into the equation. We laid it so I'll do it over here. Why is equal 2.1 a wine Times 100 free, minus free 1000.5519 And this is equal to six 0.851 wine. So now we have our observed and expected. So point by free minus six 0.8511 and we now know that the residue u'll is equal to negative 6.3211 So what does residue mean? It means that our equation was about 6.32 off the actual valley Ill. So you would use this to determine how good of an equation this is the and we are done.

Problem. 11. Which a name This number is an is equal to two plus three plus 13 plus 42 plus 15 eight plus 14 31 off eight plus two plus one is equal to 100. Question be plus weeks is equal to 10 we can see Classes are from 60 to 69 70 to 79 80 to 89 90 to 99. Hundreds toe 109 110 219 122 129 132 130 39 142 149 152 100 60. Which frequencies to three, 13, 42 58 14, 31 eight to and one which indeed. So the class is 100 too 109 preaching e The class is 1 52 1 16 which in f this percent defined by classical probability. So the probability off park you at least 1 30 is equal to eight plus two plus one over 200 which is equal to a point or 55 which in g the answer is no

In problem one were given some, like you deter for 33 1st graders that participated in a study off Children's intelligence and behavior. And we're going to be using this deter, too, concludes point estimates, forgiven parameters. Then we'll also state the estimators that I used in each case. So in part a the question we're supposed to find out the point. Estimate off the mean like you for the population off all fast graders in the school. And then we stayed the estimate er that we used. So in this case, and for the for the mean I killed for the point estimate for mean like you, the estimate er will be the pope will be me. The estimate er will be the sample mean, So the sample mean is the estimate er off the mean like you for the population. So this is how we're going to write that. We're going to see that the estimate Er, uh mu hut A estimate er off. The minute you knew, hot equals, um X bar, which is the sample mean? So in this case, the sample mean is obtained by summing up all the values and dividing that by the sample size. So in this case, we have the following valleys. We have to add all the values here which will be 82 plus 96 all the way until we get to the last item, which is 146. Then you divide that by the sample size, which is 33. So the total in this case will be 3700 53 divided by 33. And that gives this I mean off 100 that team 0.7. So the mean i Q. The point estimate for the mean like you is 113.7. Next, in part b of the question, we're going to calculate the point estimate off the AC you value that separates the lowest 50% off. Also, such students from the highest 50% men are going to stay to their signature. That will be used. So in this case, if you want to get the number off the like, you value the separatist lower the west 50% from the high 50% than the estimate. Er will be the sample medium, So the estimate er will be example median. So we write it in this form. Okay, so meet the population. Um, estimate er off them for the median equals the sample media and forced to get the sample median, we need to arrange this deter in order from the smallest to the largest. So we need to sort this out from the smallest to largest, and then we get the value that takes up the central position. And since sample size is 33 n, the sample size is 33. We will have to work out the and the I to of the I Q value that takes up the end plus one over to position. So in this case, it's going to be the 30 three plus one over to position. And that makes the t four move on to, which means we're going to be looking at the like, you value that takes the 17th our position. Once we have sorted this data from the smallest to the largest. So once you sort out the data from the smallest to the largest, you will find that the media is 113. So the value 113 takes up the 17th position in part C of the question. We're still to calculate on interpret the point, estimate off the populations than that deviation and tell which estimate er we used So the estimate er that will be used true to to estimate the population some population, standard deviation. It will be Sikma hot. Andi Sigma Heart is obtained from S, which is the sample Standard Division. And here we'll use the formula. Square it off. One over N minus one. What supplied by X I minus X box square. So we need to put a summation here so that we sum up all the values that's with be able to meet this formula. So in this case, we What we need to do is to get the square it off, the some off the falling value. So it's going to be the square off one over. N minus one. Submission off X Hi in this x bar square. So this is what we need to have here. It's squared off one off, 33 minus one multiple multiplied by this. Some off the funding. So the fast number would be 82 minus the the mean, which is 113.7. Then we square that then you add that to the second difference between the mean on the each of the values just 96 minus 113.7. Then we square. So we continue all through until we get to the last item, which is for 146 minus 113.7 square. And when you walk the Santen and simplify, you will get the value 12 with 74 So there point estimate off the populations than the division is 12.74 Just one thing here. We just need to change. The square should be here outside the bracket. Good Next. In March, De of the question, we're going to calculate a point estimate off the proportion off all such students was a cube exist exits 100. Now, in this case, we need to think off a success as i Q. That exists 100. So we have to check how many off thesis values would exit one. Hundreds have 100 to way. We have 103 on the 103 106 107. All the values that exit Exit 100 would be considered a success. So we need to count each or every value that exists. 100. And in this case, we see, actually, all the values apart from 80 to 96 99 exited, uh, 100. So that means that we'll have 30 out of 33 students that have accused that are above 100%. So So in this case, what we have to do here T is to say that p hot the estimate off the population proportion. P hunt equals the sample proportion of success. Okay, so on, in this case, we sample proportion of success equals stati, which represents the number of students who have a knack you value of 100 above, divided by 33 which is the total number of students. And when you simplify, that's going to be 10 11 and in decimal form, it is your appointed nine 091 Lastly, he part e of the question we're going to calculate a point estimate off the population coefficient of variation, and this is given by 100 signal divided by mu, so 100 sick defended by new. So we're going to complete the estimate off these relation coefficient or variation. So the estimate er it will be, ah 100 Sigma Hunt over New Hut. And we had already got in these values from the previous steps. So we just need to substitute the values that we have gotten, and this will be equal to 100 times. The meat sigma hunt is 12.74 divided by mu hot, which we have obtained as 113.7. And when you walk decent, you get that. The value will be 1274 divided by who's sorry. Yeah, 1274 divided by 113.7. And when you work that out on the calculator, you will get the value to be 11.2. So we have completed giving all the values off the point estimates for the given parameters that needed to be estimated from the population

Mhm. Okay. So we're asked a group in eighties and nineties and so on. Uh stem and leaf diagram, frequency instagram and relative frequency instagram the history and are going to have the same shape. The only difference is going to be what's in their Y axis so far further. Ado let's put some stuff onto this blank canvas. Here we go. So that's our frequency hissed a gram. Um Not the relative one but nice old shape there. As for the stem and leaf plot. This is what it's gonna look like bull right there and you'll notice that they have approximately the same shape. If you were to rotate this around, you would see that the shapes are approximately similar, although not perfectly similar. Mhm.


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