the-millersburg-school-board-is-negotiating-a-pay-raise-with-the-teachers-union-three-of-the-admin-2

Question

The Millersburg school board is negotiating a pay raise with the teacher's union. Three of the administrators have salaries of $\$ 90,000$ each. However, a majority of the teachers have salaries of about $\$ 45,000$ per year.
You are the head of the teacher’s union and maintain that a pay raise is in order. Which of the mean, median, or mode would you quote to justify your claim? Explain your reasoning.

Trinity Steen · Accepted Answer

all right, So for number 20 we&#x27;re talking about the adamant and the teachers again with E three admin that have the $90,000 salaries. And then the majority of the teachers have a salary of 45,000. But the question ships, which of the three measures would a union member 18 years? So if you&#x27;re a teacher, union member and you&#x27;re trying to talk to your admin or your superintendent or your board about possibly getting higher salaries, you&#x27;re going to use the mode as your answer as a mode happens to be the 45,000 and that&#x27;s what shows up the most. And that&#x27;s what you&#x27;re trying to fight because it was the lowest salary of the group because the median would most likely not necessarily be the 45,000. So you would want to say the mode because it was lowest salary. And as a union member, you&#x27;re trying to fight for your teachers to yet more salaries, higher salaries rather, um, and so that&#x27;s why that wouldn&#x27;t be the indication that you would want to use

Trinity Steen · Answer

$90,000 salary. But then the majority of Teacherssalaries was this 45,000. So if you think about, there&#x27;s definitely way more teachers and there are admin. So if you add Apple of their salaries and then you divide by the number of employees, both teacher and and been, that&#x27;s what&#x27;s gonna get you. Your mean, your median would be whatever is in the middle, and then the modes, whatever happens the most. So if I was a board member, which one of these three measures would I use to be talking about salaries and which toe building? To try and entice someone to come or to be, uh, working at this place? Or to be able to say, Well, these people are making a niece amount of money and the answer would be the meat, because, I mean, if I add up all of those numbers, all those salaries at that one would be the highest of the three. As as a board member, you want to have the highest salary number you can train to promote, potentially getting someone to hire to be hired

Christopher Dzorkpata · Answer

Hello. So these are the solutions. The question has been next, and, uh, I&#x27;ve also under the reason why I&#x27;m giving these answers. Okay, So I hope you find this useful. Thank you very much.

Sherrie Fenner · Answer

looking at 89. We&#x27;re doing an inversion normal because they&#x27;re giving us percentile. So in verse Nor and O r and and I&#x27;m gonna do 0.9 a mean of 44,000 But it&#x27;s damn deviation of 500. Its meaning Me. But in red, 52,000 330. And then for part B, we&#x27;re doing inverse Norm White nine. £44 6500. No, not 1000 100. Divided by this were of the 10 teachers and that equal 46 6 30 four.

Yifan Xu · Answer

or I saw the main salaries from 3 4007 are showing a table. A model that approximates the state out is given by. So this is the motto that approximate that data 42.6 minus 1.95 T well, minus point point 0.0 60. All right, so so. Question A is used to graph intimidated the critic scatter point of this data. All right, so let us use, uh, whatever eternity to plug this data. So after plotting the data is gonna be something like So the ex excess is gonna be zero two for six. Spread up evenly. And here is 40. Yeah, here, we got something like 60. All right, so this the poor, we got a little bit more than here. Something like ear here. Here for here. It&#x27;s Ah, it&#x27;s so is increasing. All right, so it&#x27;s something like it&#x27;s not that accurate, but it&#x27;s approximately like this, right? So we have points, points, points here, points their points here, points there, and points here at Central. All right, so that&#x27;s the grift from ah, graphic entity, whatever you want. And the question is how well does the mother fit the data? Or so the quick answer is the model fits the data. Ah, very well. Says all All of the points are close to the model, right? It&#x27;s all of the points of coast to the model. So fits. Well, our question see, is that according to the motto, in what year with the salary for classroom teachers, exit 16 k, so 60 k. So we&#x27;re gonna have a hard on ally from 60 K so that we can approximate the year here. So this is what we want. All right. From this graph, it&#x27;s gonna be, um, roughly the tea. Miss Rafi here, we&#x27;re gonna have this value. It&#x27;s gonna be 10 point 545 right? So the well, I have to say that the gravity is terrible because this should have bean tin something. Should I be 10 something? But it&#x27;s in the graph. It&#x27;s gonna be for something. It&#x27;s because that your autograph badly the two the two here should be do 446 and 10 here. So it&#x27;s gonna be so this value remember, that is gonna be 10.545 Just ignored the graph e. It&#x27;s terrible on the access ourself from the graph the Model X it&#x27;s 60 k. It&#x27;s gonna be at T approximately 11 years exactly 10.5 for five years. According Thio corresponds to to side than it 11. All right, so question D is that Is this model valid for long term predictions of the classroom Teacher salaries? Well, uh, whether the answer is the moderates now, valid price of the moderates not fell it for a long term prediction because it increases a lot more rapidly as time goes on that then it does in the very beginning of this model because right, so you can see that a slope of this graph increased slowly. So it&#x27;s gonna be in the future is like this, right? So it&#x27;s not gonna be feeding that the model. The model has a very go, as I&#x27;m told at, like, t ecause 17 or something which causes tomato to increase without bond as Ticos closer, closer to 16 um, which is no re elastic. So the Varda grass, until we also made that a 2016 a teacher salary would not exist. So by all of the reasons here, the motto is not valid for a non term predictions

Samuel Goyette · Answer

Okay, so we&#x27;re gonna compare the salaries of teachers in New York and Massachusetts, and we want to know if those salary are equal or not. We&#x27;re gonna use the procedure provided in page for 91 of your book. So it&#x27;s get started. The first step of this procedure is we need We&#x27;re going together over information and make our hypotheses. So that means for New York and then me for myself. Truces, you smell and for the mean of sample. So we have 70 6000, 409 and we have 73,000, 195. Both are simple, have to say is same size, which is 45. And that number is greater than it&#x27;s greater than zero. Yes, but more importantly, is greater than 30. So that&#x27;s always a good thing. And way we look at the standard deviation of both population, which think for is known eso we have seven 1008 100 1000 200. So now these are all the This is all the data we need to solve. This problem in the last part of Step one is to state our hypotheses, so h sear on H one or no hypotheses is that the means of the two population are equal and our alternative hypothesis is that they&#x27;re not equal. This means we have the to tail test. We do a tiny drawing here of a normal, which means the area we will be looking at at the end. His area here drives a bit ugly, but this does the job. So this is step one. We have our debt. Step two, we find a critical value. So it is. Get Alfa is 0.1, which means that how it felt divided by 20.5 which means that are critical values. Crit, thou oh are plus minus 1.96 You can find these in the table in your book table E and the end of the book. Step three, we compute Z so Z is the mean of her sample. So they mean your population minus the mean of Massachusetts population minus the mean of the samples, the difference of meaning of sample minus them the difference of population me, all of that divided by New York. So this tender deviation squared of Arians divided by the size of the sample. Thus there variants of the other population divided by sighs that simple to room. So this is the formula here. We know that this is a church zero. So we know that, uh, h New York and New New York minus meal as the choice is equal to zero. And then it&#x27;s just plugging did that, that we find that step one in that equation. So it&#x27;s got a little bit like their 76 1004 104 minus 70 3000 195 invited by seven 1008 100 square, over 45 plus 8200 square over 45. We put off that insight. Uh, square root. I&#x27;m not gonna do all the calculation here. You can plug that in your favorite calculator or software on your computer, and and result where Looks like this for 3209 over one point at 1600 87.1, which is 1.9 and so we can conclude. Step for is to conclude. So we know that Z is equal to 1.9, which is greater than one point 65 which is our critical value. Therefore, we reject 80 The name mule, the mean off the teacher&#x27;s salary in New York is different. Then the median salary off the teachers in Massachusetts based on that test. So quick recap we find our data. We put it all very clear. So we know everything. That&#x27;s our disposition. Step two, we find a critical value based on the Alfa Step three, we compute Z based on the information gathered in step one and step for we conclude using the Z value compute.

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