5

QUESTION ! [6 MARKSL "Variance is the average of the squarcs of the distance cach value is from the mean. While; standard deviation is thc square root of the v...

Question

QUESTION ! [6 MARKSL "Variance is the average of the squarcs of the distance cach value is from the mean. While; standard deviation is thc square root of the variance: Based on the above statement how does the standard deviation help you describe & data set? Give one cxample Marks, CO2IPO3)Atikah records the marks of Quiz for ten students from Section 0l and 02 . The Quiz marks are presented in Table TableSection 01Scction 02Calculate the sample mean for both sections und write the valu

QUESTION ! [6 MARKSL "Variance is the average of the squarcs of the distance cach value is from the mean. While; standard deviation is thc square root of the variance: Based on the above statement how does the standard deviation help you describe & data set? Give one cxample Marks, CO2IPO3) Atikah records the marks of Quiz for ten students from Section 0l and 02 . The Quiz marks are presented in Table Table Section 01 Scction 02 Calculate the sample mean for both sections und write the values using the correet notation. (2 Marks, CoUPOI) (W) Can your answer in () determine the best marks for Quiz [? Briefly explain your answer; Marks C02PO3)



Answers


Identify each numerical value by "name" (e.g., mean, variance and by symbol (e.g., $\bar{x}$ ):
a. The mean height of 24 junior high school girls is $4 \mathrm{ft}$ 11 in. b. The standard deviation for IQ scores is 16 c. The variance among the test scores on last week's exam was $190 .$ d. The mean height of all cadets who have ever entered West Point is 69 inches.

Yeah. We want to conduct a pair differences test at the alpha equals 1% level of competence testing The claim that the differences in population means near D. Is positive for D. Bar equals two and equals 20 standard deviation of differences. Five with a mound shaped symmetric distribution. We proceeded the five steps listed below two people. This problem first we check the requirements and evaluate the hypotheses. So we have a mound shaped domestic, mound shaped symmetric distribution. And so it is appropriate to use the PDT or that is it is appropriate to use a student distribution degree of freedom is n minus one equals 19 are null. Hypotheses are mute equals zero. Are alternative is much greater than zero and our alpha is 00.1 Next we can put the tests dot in the P value. So the test that is T equals D. Bar, divided by S. D. Over route or 1.78 from a tea table. We obtained that peace between .05.025 for this so we can conclude that P is greater than alpha, so we fail to reject the null hypothesis, which means that we lack evidence, McGee is greater than zero.

All right. So we have these two, uh, free Mr Tables part I asked us to find the and I've labeled these x and y just for simplicity. So for a bus was find the mean of X. Well, I'm just gonna be one times two plus two terms, three plus three times. One, That's four times 13 five times three, this whole thing, although by by the total frequency, which is 3689 20. And that will give us a value of 3.545 Starting to be Asian, where that is going to be the square root, some of want and of X, I minus X bar squared by end minus one. Was that me? In terms of our situation, that's gonna be some spurted some from one to 22 of thanks. I minus the mean, which was 3.545 squared, divided by 21. We would actually needed to do this formally correctly. We need to write out this frequency table as actual list. Somewhere in the streak. Unstable is actually a two. Then two threes, then three ones. How I did this all backwards, say to it would be to one so 11 three twos and 13 and then 13 fours than 35 It's produced the innovation of the trialist. You end up with a syndication equal to 1.184 That's a bunch calculator work. So your brother writing it out, it's just do you have to figure out the some part first, then divided by 21 that's were routed and thats much calculated work. So let's restore irrigation. And then, uh, since the two scales differed by a difference of plus one because I could make adding +10 would make it one and this one, the one would make it too, and so forth. They decided to add one toe both and then see what the result was. So the idea behind it would be like we added plus one. But then both rating systems would be could be viewed as being a 1 to 5 system, like adding plus one studies. Have you had plus wonder we could theoretically compare the distributions well, adding plus one to the ratings of why so that would change. Um, change these ratings here that's gonna result in the mean I was gonna ship the mean up to for point to one rez. As it says the problem before it was 3.21 So adding plus one changes the mean. However, before the syringe, aviation was point 568 and adding plus one does not change the Syrian deviation because it would sell the same spread. Just the values themselves have changed, but the spread doesn't change. So the the Post Star innovation would still be point by 68 and you could go ahead and calculate these using the same method I have done here in a and verify these results. It's the idea behind doing this. So like, well, we have a plus one that we could compare. The two tables are the two results. That big question. Could we, with the suggestion allow of adding plus one allow for two sample t test? And that seems like a good idea at first when you're thinking about it. Um, just from like a kind of naive stand standpoint, it seems like a good idea. But the problem is that the distance wishes color the distance between 0 to 1 and 3 to 4 might not be the same in people's minds. So, uh, is adding plus one, and using a to sample T test assumes this to be the case. Also, a T Tests is gonna measure quantitative, not quality, of qualitative donna. And again, it's the numbers words there are 125 So you would think that aQuantive That's certainly the case because of the fact that people treat these numbers as different. Here's a treat deserves is different. We there's like there's no, um it is not a 1 to 1 ratio in the scale of these two differences, even though they're both one. There's some type of potential difference on how people see the difference. These numbers, and that makes it more of a qualitative situation. Even it seems quantitative, so we can't just add one, because that's gonna assume the rating scale doesn't actually matter. And let's kind of also, the whole thing we're trying to prove is whether or not the rating scale does matter so we can be making these type assumptions when we're using a number system that's actually based upon the qualitative data of how people will see these numbers

So we're looking at the top 10 college tuitions. So we'll look at the most expensive minus the least expensive, relatively speaking, so that's gonna be our largest value, 54,410, mine is our smallest value, 50875. And we get a range of 3000 535. Uh huh. It's kind of small to be honest, for a top 10, I'll charging 50K to go there. Mhm. And then uh we can calculate the standard deviation, so I'm gonna do that in red, It's in this formula right here, So we got a sample size of 10, We'll just do that 10 right there and then we're gonna sum up the square of every sample we have And that means that we're going to square the 54,410 and the 50,000 years 75 and every value that we have between there and this is going to come out to be a pretty large number. It's kind of like quite a few numbers. So it's gonna be too 6631884 700. Okay, basically, as long as a phone number, Okay. And even longer depending on your country code and then we'll just subtract that from the sum of everything normally. So that's going to be 515,000 966. And then we're gonna square that number and just know that these two numbers are different. one is something squared and one is the sum of things squared And then we'll just divide by 10 times 10 -1 since that's what the bottom part of our formula says to do. And after doing a lot of number crunching, This turns out to be 1043 and 15 cents for our standard deviation. Now the variance is the standard deviation squared, So that is going to be one million 88153 and 82 cents groups. Okay. Yeah. And just know that we only sampled 10 colleges, so we can't really say anything about the other 900 or 1000 colleges that are in the U. S. Since the top 10 is surely not a good representation of the whole United States College system.

The following is the solution for # seven, Number seven, which involves the archaeology or regional distribution of raw materials and comparing it to a current excavation site. And I did a little preliminary work here. First I um was we were given the absurd value so I just copy those down and then I found I had to find the expected values and I use those percents that were given. And I multiplied by the sample size to get the expected value. So I took the 61.3% or .613 and I multiplied by 1486. And I got that's where I got this 910.918 and that's what I did for all these percent. And I got these values here. So I needed that in order to find and what I like to do on these is kind of look at these numbers and compare them. And if they are really, really close something that these two distributions are are are going to be roughly the same. And in this case they look pretty darn close to the same, like 53 53 1 97 and 1 94 and so on. They're pretty close to the same. So, I'm thinking that we're gonna get a pretty high p value here, pretty small chi square value because they're so close together. Um but that's just a hunch. All right, so let's do it mathematically. So, first portion of this is finding the significance level that's given to you. It's always the alpha value. So, the significance level here is 1% of .1. The second part of this is writing the Nolan alternative hypotheses. And you can wear these however you want. But basically, the null hypothesis is saying that these two distributions are the same, and the alternative is saying that they're not the same. So in this case we can say for the knoll the regional distribution of raw materials fits the distribution at the current excavation site. And then I'll just shorthand the alternative is just saying that it's not so regional distribution of raw materials does not fit the distribution at the current site. Okay, So the next part, we need to find the chi square value and we're gonna find out with technology, so we're actually going to kind of come back to that. The also another part of this is finding the expected values, which we actually already did, and we just want to verify that all these expected values are greater than five and they are. So that's one of those conditions for inference that all the expected values need to be greater than five. And then it also asked us what distribution we're gonna use, we're gonna use a chi square distribution, obviously because it's a chi square goodness of fit test. But then we also have to say how many degrees of freedom In this case, there are 4° of freedom because there are five categories. So 5 -1 gives us the degrees of freedom of four. Okay, so from here we're going to be in the technology. So again, you can use I'm using the T I 84 but you know, you can certainly use Excel S. P. S. S sas are, you know, whatever statistical software package you want, I find T- 84 to be pretty easy for elementary stats. Okay, so I went ahead and took the liberty and L one, I put the observed in an L two I put expected and then if you go back to stat air over to test and it's it's close to the bottom. So I went up first and it's the chi square G. O. F. Test and that stands for goodness of fit test. And assuming you put observed in no one you're going to change that to L. One expected will be L. Two and then your degrees of freedom, like I said, we'll be four and then we're gonna calculate that thing and that gives us everything we need. So that chi square value, that's right up here, that's what we want. So it's about 40.198 So like I thought it's a pretty small chi square value, 0.198 You know, it's gonna be pretty pretty much smaller than anything we're going to get. And we are also given the P. Value and I don't know if you saw it but that's a pretty much as big as you can get. So 0.995 Very large P. Value. So 0.995 And that P value is obviously greater than alpha. It's definitely greater than that 0.1 that we were given. And any time the P values greater than alpha, we fail to reject H. nine And we failed pretty hard that time. Right? So we're not definitely not going to reject because that is a very very strong P value. Very very large P. Value. And the last part of this is party. It's um stating a formal conclusion using the word. So again there are different ways of wording this and I'm gonna say there's a double negative here. But this is the way the ap exam likes it. So it says there is not sufficient evidence to suggest that the regional that the regional distribution of raw materials is different than the current excavation site. Okay, so that's the formal conclusion would come up with. Whenever we fail to reject meaning, there is not sufficient evidence to say that these two distributions are different.


Similar Solved Questions

5 answers
Chi Square Lambda olive oil is touted as the World s most expensive olive oil, dollars or more twelve-ounce bottle typically costs fifty blind taste test, group of food experts tasted three premium olive oils; one ofwhich was Lambda olive oil. When asked to pick the Lambda olvve oil, 84 got it right and 87 got it wtong:Ifthis group were just guessing how many people (out of171) would you expect to guess correctly? (4pts) (Showyour worki)
Chi Square Lambda olive oil is touted as the World s most expensive olive oil, dollars or more twelve-ounce bottle typically costs fifty blind taste test, group of food experts tasted three premium olive oils; one ofwhich was Lambda olive oil. When asked to pick the Lambda olvve oil, 84 got it righ...
5 answers
Ngel; + {ct {~4(v) fat X.hlsva 7vld k(k] 50y {ha ( cplon: e4 Ydp? 4n4 ~A01t
Ngel; + {ct {~4(v) fat X.hlsva 7vld k(k] 50y {ha ( cplon: e4 Ydp? 4n4 ~A0 1t...
5 answers
A bacteria population grows with constant relative growth rate. It started with 1,000 cells, and grew to 30,000 cells in seven hours: Find the population growth constant. (6) When will the population reach 200,000 cells?
A bacteria population grows with constant relative growth rate. It started with 1,000 cells, and grew to 30,000 cells in seven hours: Find the population growth constant. (6) When will the population reach 200,000 cells?...
5 answers
Mustard gas, S(CHzCHzCI)z can be made at room temperature as shown: sClzlg) + 2 CzHalg) = SICHZCH2CI)zlg).particular experiment 0.804 M of SCIz and 0.588 M CzHa were mixed. At equilibrium; {S(CHzCHzCI)z(g)} was 0.2346 M. What is the value of Kc for this reaction?(value 296)
Mustard gas, S(CHzCHzCI)z can be made at room temperature as shown: sClzlg) + 2 CzHalg) = SICHZCH2CI)zlg). particular experiment 0.804 M of SCIz and 0.588 M CzHa were mixed. At equilibrium; {S(CHzCHzCI)z(g)} was 0.2346 M. What is the value of Kc for this reaction? (value 296)...
5 answers
Chemist makes 410, ml mercury(T) chlonde (IlE_CV) working solutlon by adding distlled water 120,ml f a $,50 colubiam mercury(I) chlonde wator;stockCalculate the concentration the chemist $ workIng solution Round vour aosheslonificant digits .
chemist makes 410, ml mercury(T) chlonde (IlE_CV) working solutlon by adding distlled water 120,ml f a $,50 colubiam mercury(I) chlonde wator; stock Calculate the concentration the chemist $ workIng solution Round vour aoshe slonificant digits ....
5 answers
3. (8 points) You want to test the following hypotheses using a level of significance of 5%: Ho: T2 T [ 20.25 Ht: T2 TI < 0.25 The sample data are: n] 200, Xl 40 n2 500, X2 = 240 What are the sample proportions, p1 and p2? b What is the estimated variance of pz p1 What is the estimated standard error of p2 - pI_ d. What is the attained value of the test statistic? What is the p value? € Can we reject the null hypothesis?
3. (8 points) You want to test the following hypotheses using a level of significance of 5%: Ho: T2 T [ 20.25 Ht: T2 TI < 0.25 The sample data are: n] 200, Xl 40 n2 500, X2 = 240 What are the sample proportions, p1 and p2? b What is the estimated variance of pz p1 What is the estimated standard e...
5 answers
Problem Compute the exact length of the curve y=xs from X= to x = 8 [You need to use substitution to calculate the resulting integral]:
Problem Compute the exact length of the curve y=xs from X= to x = 8 [You need to use substitution to calculate the resulting integral]:...
5 answers
Criticnl Numbcrs;Palcntial inllection points:Complctc TableInicrthueSign of f5go 7LonalusionGrph the function labcling all interccpl(s}, usymptotec(s} relativc mimmax, and inilection points,
Criticnl Numbcrs; Palcntial inllection points: Complctc Table Inicrthue Sign of f 5go 7 Lonalusion Grph the function labcling all interccpl(s}, usymptotec(s} relativc mimmax, and inilection points,...
5 answers
What is the most eflicient way to cool & solution in a flask below room temperature?Many chemical reactions occur vcry slowly at room temperature; they are to increase the rate of the reaction , The process of can be used t0 scparate two liquid organic compounds that have boiling points less than 30" € apart
What is the most eflicient way to cool & solution in a flask below room temperature? Many chemical reactions occur vcry slowly at room temperature; they are to increase the rate of the reaction , The process of can be used t0 scparate two liquid organic compounds that have boiling points less th...
5 answers
For which values ofthe parametrc cun€Yut+t Cosio (Enter Your bnewer 4sinq interval notation /,< (9,0),[0,6), [0,6] or [0,6J)ccncatt
For which values of the parametrc cun€ Yut+t Cosio (Enter Your bnewer 4sinq interval notation /,< (9,0),[0,6), [0,6] or [0,6J) ccncatt...
1 answers
Construct an argument using rules of inference to showthat the hypotheses “If it does not rain and if it is not foggy,then the sailing race will be held and the lifesaving demonstrationwill go on,” “If the sailing race is not held, then the trophy willnot be awarded,” and “ The trophy was awarded” imply theconclusion “It rained.”
Construct an argument using rules of inference to show that the hypotheses “If it does not rain and if it is not foggy, then the sailing race will be held and the lifesaving demonstration will go on,” “If the sailing race is not held, then the trophy will not be awarded,” and “ The trophy ...
5 answers
If a computer does a single bit operation in 10-9seconds and if a problem requires n bit operations to calculate a solution, what is the maximum n can be to solve the problem in 1 second? (10) (logz102)logz10910910-9
If a computer does a single bit operation in 10-9seconds and if a problem requires n bit operations to calculate a solution, what is the maximum n can be to solve the problem in 1 second? (10) (logz102) logz109 109 10-9...

-- 0.018053--