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Investigating how many jobs are created by new 1.A business analyst Using a sample of 101 start-upS, business start-ups across Europe: find an average of 63 new job...

Question

Investigating how many jobs are created by new 1.A business analyst Using a sample of 101 start-upS, business start-ups across Europe: find an average of 63 new jobs created with & sample standard they deviation of 29_a) Construct a 90% confidence interval for the mean number of jobs created. [25 Marks] b) Carefully explain what this confidence interval implies. Would higher degree of confidence produce a larger or smaller interval? [25 Marks] c) The researcher also has a breakdown of the da

investigating how many jobs are created by new 1.A business analyst Using a sample of 101 start-upS, business start-ups across Europe: find an average of 63 new jobs created with & sample standard they deviation of 29_ a) Construct a 90% confidence interval for the mean number of jobs created. [25 Marks] b) Carefully explain what this confidence interval implies. Would higher degree of confidence produce a larger or smaller interval? [25 Marks] c) The researcher also has a breakdown of the data, showing that 60 manufacturing companies created an average of 68 new jobs with a sample standard deviation of 31. The 41 non- manufacturing companies created 57 new jobs with a Sample standard deviation of 21. Test whether there is a difference in the variance of new jobs created between the two sectors [25 Marks] d) Test whether there is a difference in the mean number of new jobs created between the manufacturing and non- manufacturing sectors at a =0.05. Use the results from the equality of variance test above to make the necessary assumptions on the standard deviation of jobs created in both sectors. [25 Marks]



Answers

For large U.S. companies, what percentage of their total income comes from foreign sales? A random sample of technology companies (IBM, Hewlett-Packard, Intel, and others) gave the following information. Another independent random sample of basic consumer product companies (Goodyear, Sarah Lee, H.J. Heinz, Toys " $\mathrm{A}$ " Us) gave the following information. (Reference: Forbes Top Companies.) Assume that the distributions of percentage foreign revenue are mound-shaped and symmetric for these two company types. (a) Use a calculator with mean and standard deviation keys to verify that $\bar{x}_{1} \approx 51.66, s_{1} \approx 7.93, \bar{x}_{2} \approx 33.60,$ and $s_{2} \approx 12.26$ (b) Let $\mu_{1}$ be the population mean for $x_{1}$ and let $\mu_{2}$ be the population mean for $x_{2} .$ Find an $85 \%$ confidence interval for $\mu_{1}-\mu_{2}$ (c) Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the $85 \%$ level of confidence, do technology companies have a greater percentage foreign revenue than basic consumer product companies? (d) Which distribution (standard normal or Student's $t$ ) did you use? Why?

Once again, welcome to a new problem. This time we're dealing with confidence confidence intervals and the confidence intervals. Looking at his for proportions. So if you have a population of subjects of people, this population can have P which is the same as the population proportion. You know, this is the same as the population proportion. And within that population proportion you have P had which is the same as the sample proportion. And you can always make predictions Using P uh on P hurt for example, if you wanted to I predict the percentage percentage of females. Yeah in a college campus you can use pr to predict P. The problem though is in estimation there is likelihood good of error. So this is the likelihood of making an error. Mhm. In estimation. Therefore, confidence level, illicit trust in the prediction outcomes for both proportions and means. So then you know you have period plus minus E. We where he is the margin of error and then the E will be the same as Z alpha over to Body called P Hut 1 1 Speed Hut, Oliver, N ZF of two for 95% confidence will mean that this middle parties for 95 And then each one of the Tales is .025. That's each one of the tails. And so z off over 24 95% confidence is 1.96. Of course you have two sides. This would be the negative side in this positive side. 1296. And the reason for that is because we have a plus and a minus. So coming back to these problems, we have surveys of employees. Yeah. In multiple industries uh revealed the uh type of industries which are under stuffed. So the type of industries which are understaffed. And we're seeing that for example, in the government sector, the government sector, the understaffing dessert 37% based on respondents information. And then also we have in the health sector uh 33 under stuffed. And this again is based on responding to information. And and then we have understaffing in the education sector where the level of Under staff in his 28 and the stuffed. Mhm. And all this is based on 2010 U. S. A. Today. Yeah, I think perhaps assume assume 200 walkers Or salvage. So we're making an assumption that 200 workers, we solve it. And then but they were going to say uh determined become in 95 confidence interval mm mm For proportion in order of walkers by industry. Mhm. Uh Under stuffed. And then the body was saying, mhm assuming similar similar sample sizes by industry. Yeah, determined the size. Oh, this sample that guarantees guarantees imagine of error. Imagine most zero oh .054. Each of the we yes confidence. Mhm Intervals. Each of the three confidence intervals. So on this one will start by saying we have three industries. And so what we're saying P. R1 equals two 0.37 P. R two equals 2.33. And perhaps three is the same as .28. The sample size is 200 At 95% confidence. We know that the ALF of two is the same as mm Z of .25. And this gives us 1.96. This is a critical value critical value from the table. This is a critical body from the table. So start with the government sector and say he had plus minus margin of error for the government. So this is the hot plug plus zero for 2. Um These er for the two is the same but then the proportions are gonna be different. So this is pr 11 minus P. Hard won all over him. Then we'll go ahead and Plug in the numbers so 0.37 plus -1.96 vertical on p hub Is going to be .37 1 -37. All over 200. And so the confidence uh interval in this case for the government becomes estimated as approximately between points. What was 30% to 43%. And then also yeah we have healthcare, we have healthcare and flow healthcare you can see that. Mhm. Won't have pr would rather this should have been He had he had one. Yes that should have been here. And then for healthcare it's we have two plus minus E. Hell and this becomes we had two plus minus Z. L. For two articles Peer to one Rider spear to over end. So pr two is 20.33 plus minus 1.96. Radical points through to me 1 -33 Oliver N. And so the confidence interval okay for health becomes the same as its approximate 0.26 for it to points three line 52. Yeah that in the next part we have education and so P hatch three plus minus E. Education. That's the era of the education level. So this is a three plus minus zero Fortitude Radical Piazza We've won one is pr substitute all over in. So there we have three is 30.28 plus one is 1.96 44. Mhm 0.28 1 -18 all over again. Mhm So the confidence interval and this time it's for education it's going to be approximately the same as .2178 2.342. So that's the first part and then put the Given the heir to the point of five. We understand that mm and is the same as 04 over to want to square that pizza hut one. My spirit. All those E squared and going to go ahead and plug in are specific number assume for estimates some things Period his zero five and so what's going to happen is that Uh huh Gonna take those er for two We want to take this year off of two and say 1.96 squad And then .45 we need another .5. We also have the denominator mhm The denominator when it's when it's rounded up Uh huh You know, just just to make sure we got the right numbers. So we're saying looking for the the margin of error for the three intervals, we're looking for the sample size. So for this one yeah, we already have the margin of error. So this one is also going to be the P had sorry, the p heart The pr is .37 because it's going to be the same for all the industries. So .37 So we change these numbers right here. Change these numbers. So this is Points 37 and this is .37 and so we end up mhm With the denominator 0.0 and All five Squared and so or sample size Sample size becomes approximately descends for 43. So I hope you enjoyed the problem. Well, this one should have been one minus so just remember that this is one mix and this is a square. So I hope you enjoy the problem. Feel free to send any questions or comments. Mhm Hope you enjoy the bargain. Feel free to send any questions or comments and have a wonderful day

Following a solution number 46. And we're gonna look at how outliers affect certain datasets whenever sample sizes are different. So we're giving a simple data set where the population mean is 50 and the standard deviation for the population is 10. and we're asked to find a 95% confidence interval for that Data set. So I'm using technology here just to save some time. So I'm using a T- 84, but you can use whatever technology or the formulas if you want. Um and if you go to stat and then I'm gonna go ahead and say edit now. L one, I'm gonna use both columns here, L one and L two but L one is the first data set and you see actually is the the exact same. So these 12 data values are exactly the same as L two until you get to a certain point. But this is the small data set that we originally start with. So L one Only has 12 data values. So there they are, went ahead and punched him in and um we're gonna go to stat tests and it's the seventh option here, the Z interval since we know the population standard deviation and keep it ever done on the data. Uh Since we have an actual data set, Sigma's 10 to list in this case is going to be L one. That will change that later whenever we get to the second part of this question and then the sea level frequencies one always and then the sea levels 10.9 fox that asked for a 95% confidence interval. And whenever we calculate now keep this X. Bar in mind 50.25 I'll leave it up here. But Um here's our interval here, 44.592 and 55908. Let's go and write that down. That's really just the first part, is a simple confidence interval. We don't even need to interpret it because they don't think there's a word problem associated with this, But it's 44 592 On the lower bound, and then the upper bound is 55.908. Okay, so that's our Confidence interval. Now, it says, Okay, let's pretend like the 41 and that data set is changed to a 14, and we need to confirm that it is in fact an outlier. Okay, well let's see what they're talking about. So stat edit And it's saying that this 41 here is changed to a 14, so let's go and change that and let's see what happens. I'm gonna go ahead and calculate the one bar stats here. Now there are a couple of ways that you can determine if something is an outlier. You can see if it's two standard deviations above or below the mean. So if you were to do that, you remember the standard deviation was 10 now it gives you something little different here, but we're assuming that it's 10. Um So two standard deviations would be 22 times 10 is 20, so 48 minus 20 is 28 14 is significantly less than that. So anything above or below? Two standard deviations from the mean, but there's a better way, it's the inter quartile range method, So what we do is we take the inter quartile range which is Q three minus Q one, we multiply it by 1.5, and that gives us a number to work with, So let's go and do that first. Um Yeah, so the inter quartile range, remember as Q three minus Q ones, that's 53 minus 435 in this case which is 9.5. And then we're gonna take 1.5 times 9.5. And that gives us 14.25. So this is a little bit more robust than the two standard deviation deals because we don't know if this is normal actually, so so this is good, so 14.25 And then what we do is since it's on the lower bounds of 14 is smaller, we're gonna take Q. One which is 43.5, we're gonna subtract that 14.25 And that gives us 29.25. And since 14 is less than 29-5 than it is in fact an outlier. So it's an outlier. In both cases it's definitely two standard deviations below the mean and it's 1.5 times the intercourse, our range below the first quarter. So in both cases it's an outlier. So that's the confirmation. Now, we're going to find the new Um 95% confidence interval. Okay, so let's go back to stat tests and it's that seventh option? The z interval. Okay, so everything again is exactly the same. But remember that 41 is now 14, so it should change it a little bit and it does. So 42.342 and 53.658. Let's go and write that down and then let's compare. So 42 .342 All the way up to 53 .658. And it asks what you know, how do these compare? Well, if you look at the first confidence interval to the second confidence interval, everything's been shifted down a couple units. So that confidence interval gets pulled just like the mean would be it gets pulled towards that outlier. So the confidence level or the confidence interval ci with the outlier is shifted down or pulled down towards the outlier? Okay. It's also, you know, a little bit bigger um because that variation is gonna be a little bit better, but the main thing is that shifted down because that mean is not robust, it's it's pulled towards that outlier and the mean remembers the point estimate. Okay, so that's part c. So now we go back and we're actually going to change change that back, so stat Edit and then let's go and change this back to 41. Okay, so the next part Were given another data set. Now let's go ahead and write this down. So the X bar the mean for the smaller data set, where it was just 12 data values was 50.25. That's what it asks for here. So 50.25 and then the large data set. That's where I put it in L. two now. Already populated in there. I already punched it in. But here are it's you know significantly bigger. I don't remember how many Data values. 30 or so. Yeah. So 36 data values. All right. So that's the difference there. So let's just make sure that it's the same mean. So let's change this to L. two. Okay? So 50.25. So the sample mean is exactly the same. So 50 point 25 So that's all we do there. So the sample means the same and you may think that the confidence interval needs to be the same now but we're gonna see here in a second it's not so we're gonna make a 95% confidence interval for the larger data set. So if we go back to stat Tests and again it's that 7th option. The z interval. Okay, this is all good. Except this time. The list is L two. Okay. And then we calculate and it gives us this 46.983 and 53.517 46,983, I'm sorry. Oh yeah, that's right. 46.983 2 53.517. Okay, So what does that mean? Well, it's if you look at this confidence interval of 46 to 53 compared to that first confidence interval, 40 40 55 it is a narrower confidence interval now, it's the same confidence level, we're still 95% confident. But what changed? Well in went from 12 to 36. So what does that mean about the width of the confidence interval within? Well, as in increases the width of the confidence interval decreases because that margin of error is going to decrease because you're dividing by a bigger number. So as in increases the margin of error decreases, which means the width of the confidence interval will also decrease, and that's shown there. So the X bar did not change, right? So nothing changed their with those point estimates, the only thing that changed there was the margin of error. Okay, so this last few parts, we basically just do what we just did. So, um we're just working with the second data set and we're gonna change that 41 to 14 for the second dataset. Okay, and again, we're going to confirm that it is in fact an outlier. So let's go back to couch one of our stats. Okay, so 49.5 as the means, so if you think of two standard deviations, that would be 29.5 um and 14 is less than 29.5. Or you can do the inter corte range, that's a little more robust. So I'm going to the inter corte range, that's Q three minus Q one, which is 13. Okay, so we're confirming that it's an outlier city. Inter quartile range is 50 6 -43, which is 13 And I take 1.5 times 13 to give me 19.5 and then I take Q one, which is 43 minus that, 19 5, That gives me 23.5. And since that 14 is less than 23, it is in fact an outlier. So, again, it's an outlier. In both cases it's two standard deviations Below the mean, which in this case is fine because the sample size is big enough, but the intercourse, our range is usually the more preferred method. Now we're gonna make a new 95% confidence interval. Okay, so we go back to stat tests and it's that seventh option. Okay, so all this is good. So remember I had that 41 change to 14 calculate I get 46.233-52.767. So let's write that down and then we can compare real quick. So 46 233 All the way up to 52 767. So that's the new 95% confidence. And so how did that change this here? Well, yeah, 46.9 and it got pulled down to 46.2 and this one is 53.5 and that got pulled down to 52.7. So it did get pulled down a little bit, but not nearly as much as whenever the sample size was 12. Remember this one it got pulled down, you know, a full 2 2.5 units, whereas over here it just got pulled down. You know, I don't know, just a little over a half a unit. And the reason for that, the reason why it didn't get pulled down as much is because that sample sizes larger, the larger the sample size, the less influential those outliers can be. So what happened here? The outlier pulled the confidence interval down a bit but not nearly mm as much scroll down a bit as when And equals 12. Okay, so the larger the sample size, the less influential those outliers will be.

Okay, so in problem 12 were given the following information. Hey, random sample of 50 retired men haven't average number of jobs they had during their lifetime of 7.2 at a population center. Deviation This 2.1 port, eh asks us to find the best point estimate of the population. Mean so the best point estimate of population mean is the sample me. So in this case, the best point estimate of population this 7.2. Because that is we sample me. Harpy says to farm the 95% confidence interval of the need number of jobs. So to do this, we need to know this formula right here, ex far, plus or minus Z of Alfa over two times Sigma over the square of Ed. So we have everything that we need for this formula except for that Z score. So in order to find her Z score, we need to find what Alfa is. So Alfa is just one minus our confidence level, which in this case is 95%. So it's going to be one minus 10.95 which gives us zero point zero, but And since we're doing a confidence interval and we want both sides of the interval. You have to divide Alfa by two and we get zero point zero thio. But so he need to find the easy score zero of 0.2 But so, using your calculator or your Z tables, you could find what Z value is Oven alba 0.0 to 5 and you should find 1.96 is U Z score. So once we have our Z score and we have all the values we need to find a 95% coffins in a row. So to find our cooperative, all we have our ex far, which is 7.2 plus or minus. Arazi score 1.9 sets times sigma over the square of it. I'm gonna calculate this side first, so we get 7.2 plus or minus zero point five p to one. And then I confined upper limit and the lower limit of my confidence interval. So the upper limit is 7.2 plus zero point by 8 to 1, and the lower limit is going to be seven point two. My guess zero point by a two. What Once you calculate both of those, you won't get 7.782 for the upper limit and you will get sex toy 618 or your lower lip. So our final answer this is 95 herself. Confidence interval ISS 6.61 It two 7.7. Okay, two. So heart see is very similar to Barbie. Except now we're just finding the 99% confidence interval instead of the 95% confidence interval. So we have to do the same thing. We need to find Alfa just like me. One minus 0.99 And then again because we're doing Interval. We need two sides. So we're going to divide Alfa by two. Well, that 0.0 All right, and then we need to find our Z score. Bye, Alfa. 1005 Who was two point by seven sense. Now we have all of our values. You can just walk them in. We have seven. Wait too. Lost your minus two. Wait by 76 times 2.1 over the square root of 50. And again, I'm going to do this right side first. So I've said in qui tu waas remind us 0.76 bye zero Very. And then I just leave my upper limit and my lower limit. Your parliament is where to be 7.2 plus 0.76 503 and my own room. It is more to the 7.2 minus zero boy 76 by 03 So my upper limit is going to be 7.965 My lower limit is going to be six 0.435 So my final enter or part C is my 99 her say confidence interval ISS six weeks 435 to 7.96 Huh? So party asks us which interval smaller and they want us to explain why. So I've written both of the intervals and if you look at them, you can see which one is wider. You can see which one has the lower lower than the lowest lowest our interview boat and the highest high edible animal. So if you look at that this 95% Cochran is inedible is the smaller interval now Why is that? Why is the new 35% confidence terrible smaller than the 99% copy tenable. Well, if you think about it, the 19 line percent confidence interval has to be wider than the 95 because to be more confident that the true population mean falls within the interval, you need to have more values within that interval. And if you draw yourself the normal distribution and you are showing 95% confidence interval, that means because we divided that Alfa by two you have zero point zero 25 on either side of your area guns. If you are calculating in 99% confidence interval, your interval is going to be wider because all you have on the outside the zero point zero Nero bye on either side. So that 99% confidence interval includes the 19 5% copy example because in order to be 99% confident as opposed to 95% confidence off the true mean lying within your interval, you need to include more values

Are null hypothesis is muse equal to 0.2. And our alternative is that you is greater than 0.2. We're conducting this test at the 5% significant level. With a sample size of 20 and a standard deviation population of 0.42. The average is going to be calculated by adding up all the numbers that we have divided by the sample size. Since we have a sample size of 20, we're gonna be adding up 20 numbers And this number is going to turn out to be 0.295. Next up, we're gonna be calculating the Z score. Z score is gonna ready to here in blue. It's the difference between the two averages the sample and the population divided by the standard deviation population divided by the sample size square rooted. So this is going to equal 0.295 value. We just got zero point to the value. You think it is? Our value that the population is? So we have a 0.42 Right here and the square root of 20. Since there's 20 samples? Yeah, This comes out to be approximately 1.01. Okay, so now to find out our P value. All right, We find that the probability that Z is greater than 1.01 because we have this part right here. He was greater than 0.2. Okay. Ah This is going to be equal to out whips. Yeah, This is going to be the same as 1- the probability that Z is less than 1.01. So we're just looking at the other side of the line. So if we had a graph chop that off there, we were initially looking at this part right here and what this equation does is get us the right half. Okay, So what is one? What is P zero or what is this right here, We're gonna look in table two and we see that it is 1 -0.8438. And this is your .1562. Okay, So at the 5% significance level, this is clearly bigger than 5%. Therefore we failed to reject the null hypothesis. At the 5% significance level, there's not sufficient evidence to show that the mean Is greater than 0.2. Mhm. Mhm. Now, for a normal probability plot, we see that we have a fairly linear line right here and uh there's no outliers. There's a couple thoughts that are kind of a little bit out there, but nothing that drastically affects the normal probably curve. So this indicates that the distribution is normal and that the population has a normal distribution rather. And for the boxing plots We find that the median is going to be 0.35 first quartile is going to be 0.5 2nd quartile or sorry, the third, there is no second quarter of this technically is cute too, but it's weird to think about it that way. This one is a 0.65, The IQ. R. is going to be one of these two values subtracted from each other, so 0.6 And then the maximum is 0.9. Yeah so then we can make our box plots and as it turns out so this is what it looks like the median right in the middle. Q one is up here, Q three is on this right side. This total length is 0.6 And our maximum is at 0.9.


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A "swing" ride at a carnival consists of chairs that are swung in a circle by 15.6 m cables attached to a vertical rotating pole, as the drawing shows. Suppose the total mass of a chair and its occupant is 119 kg. (a) Determine the tension in the cable attached to the chair. (b) Find the s...
5 answers
2.A mass spectrum of an organic molecule showed the following parent peaks [m/z (intensity)]: 132 (45%), 133 (3.0%) 134 (0.27%). Propose a molecular formula consistent with these facts and calculate SoapBar:MF = ?SoapBar = ?
2.A mass spectrum of an organic molecule showed the following parent peaks [m/z (intensity)]: 132 (45%), 133 (3.0%) 134 (0.27%). Propose a molecular formula consistent with these facts and calculate SoapBar: MF = ? SoapBar = ?...
5 answers
Homework 10.5 A telescope has an objective mirror with a 508 cm diameter. Determine its angular limit of resolution at a wavelength of 550 MI . How far apart must two objects be Onl the surface of the Moon if they are be resolvable by the telescope? The Earth-Moon distance is 3.844 x 108 How far apart must two objects be on the Moon if they are to be distinguished by the eye? Assume a diameter of 4.0 mm for human pupils.
Homework 10.5 A telescope has an objective mirror with a 508 cm diameter. Determine its angular limit of resolution at a wavelength of 550 MI . How far apart must two objects be Onl the surface of the Moon if they are be resolvable by the telescope? The Earth-Moon distance is 3.844 x 108 How far ap...
4 answers
Q1/ Draw the complete photochemical reactions of photosynthesisQ2/Compare photosynthesis and photorespiration in terms of 1- Light energy 2- Location 3- NADH2 4-Outputs((I hope that the line and the solution are clear))
Q1/ Draw the complete photochemical reactions of photosynthesis Q2/Compare photosynthesis and photorespiration in terms of 1- Light energy 2- Location 3- NADH2 4-Outputs ((I hope that the line and the solution are clear))...

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