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The following data shows the yearly income distribution of sample of 200 employees at MNM, Inc Yearly Income (SLOOOs) 20 - 24 25 _ 29 30 _ 34Number_of Employees40 -...

Question

The following data shows the yearly income distribution of sample of 200 employees at MNM, Inc Yearly Income (SLOOOs) 20 - 24 25 _ 29 30 _ 34Number_of Employees40 - 44What percentage of employees has yearly incomes of more than $35,0002 Is the figure (percentage) that you computed in Part (a) an example of statistical inference? If no, what type of statistics does it represent? Based on this sample_ the president of the company said that "45% of all our employees' yearly incomes are ov

The following data shows the yearly income distribution of sample of 200 employees at MNM, Inc Yearly Income (SLOOOs) 20 - 24 25 _ 29 30 _ 34 Number_of Employees 40 - 44 What percentage of employees has yearly incomes of more than $35,0002 Is the figure (percentage) that you computed in Part (a) an example of statistical inference? If no, what type of statistics does it represent? Based on this sample_ the president of the company said that "45% of all our employees' yearly incomes are over $35,000. The president's statement represents what kind of statistics? What percentage of employees of the sample has yearly incomes of $29,000 or less? How many variables are presented in the above data set?



Answers

Sample annual salaries (in thousands of dollars) for employees at a company are listed. $\begin{array}{lllllll}42 & 36 & 48 & 51 & 39 & 39 & 42 \\ 36 & 48 & 33 & 39 & 42 & 45\end{array}$ (a) Find the sample mean and the sample standard deviation. (b) Each employee in the sample receives a $5 \%$ raise. Find the sample mean and the sample standard deviation for the revised data set. (c) To calculate the monthly salary, divide each original salary by $12 .$ Find the sample mean and the sample standard deviation for the revised data set. (d) What can you conclude from the results of (a), (b), and (c)?

So in this question, were given sample annual salaries in thousands of dollars and in part they were asked to find the sample mean and the sample standard deviation, which is given by this for Mila over here. So to find the sample mean and standard deviation, we basically use thes formulas. They substitute all the values of X, and our sample means is equal to 41 point 6923 thousands of dollars. Our sample standard deviation is 5.99 rounded to two decimal places. And so this is our answer to part in now for part B, we're told that each employing takes $1000 race. So you get $1000 races. Since all of these air in thousands of dollars, we're gonna add one. So the soldiers on 41 36 all the way up to 48 and then we're going to calculate our sample mean and standard deviation, for example, mean in this case is 42.6923 and our sample standard deviation actually stays the same at five point 99 Now, in part C, we're told that each employee takes a pay cut off $2000. So all of our values, you are going to decrease by two. So this is going to become 37 38 so on. And in that case, our sample mean is basically going to decrease by two from the initial. So we're gonna have 39.69 on our sample. Standard deviation remains the same at 5.99 So we have our answers to part A B and sink. Now let's move on to part Dean. So in part D were asked what we can conclude from the results of A, B and C So basically what? We can conclude this, that when we had or subtract a constant value from the data when we add or subtract a constant valley from our data, our mean well increase or decrease. Why the same amount So say we add or subtract an amount key from the data. Are minnow increase or decrease by the same amount? What the standard deviation remains the seen? Because the variation the data is constant. It just increases or decreases all the data just cool up or down by the same amount. So the standard deviation remains the same, but to me increases or decreases by the value that we had or subtract the data.

And this problem and talks about Ah, boss. He makes 200,000 year. And who hires employees who made $20,000 a year, So we don't know how many employees there are. So the total amount of money that gets paid out is 200,000 plus 20,000 times the number of employees. So to calculate the average salary with this same divided by the total number of employees, Which is X for the employees, Uh, plus one for the boss. OK, so that's our equation, Um, wants us tow right that function in and grab it. So basically, we have in, ah, vertical ass in tow, X who once I do that. So the very classic that will actually be X equals negative one. Okay, so that's that's interesting. Um, so the soup again could I get that a race through quick. Perfect. Um, so we have a very classic X equals negative one. And we also noticed that, um, since the degrees of both these functions Air one, we're gonna have a horizontal s in tow at 20,000 which kind of makes sense. Um, as as we take the average with more and more employees. It should get closer and closer to 20,000. Um, and then it's gonna have a why intercept if you plug in zero. Ah, then the Y intercept will just be at 200,000. If that makes sense, because if there are no employees, then the only money that's being made is by the boss. Okay, so and so that now the only numbers that matter just as it approaches as exit purchase. Infinite number of employees the average salary gets closer and closer to 20,000. OK, so that's our That's our graphs. That's our right and grab that function. So, for Part B, it just says, If there's three employees, what's the average salary? Well, if you just plug in three, you'll see 200,000 plus 60,000. That's 260,000 Um, and then divided by for him. Total employees. Anyone was here, there on that. That number is going to be 65,000. Not a very good representation, since most of the employees they're just making 20,000. And then it said if you if it was 30 employees, well, that's gonna be 800,000 because 30 times 620,000. Okay. And then we're gonna divide that by 31 total employees, and that's gonna give us a number a little bit better suited to what we have going on. So it's gonna be 25 806 45 Yes, actually, I think that's exactly it. We'll see. And then, uh, part see is just a little critical thinking it. So is average salary the best way to talk about this? And, um, I'm not too sure. Like if you're talking about it Ah, you might somehow want to indicate that there is one person who makes 200,000. Um, so But if you really want to talk about what The average employee Well, most of the employees are making 20,000. So I would probably for part C if you wanted to talk about using the median to describe the average salary or maybe even the mode. Um, I would probably if I if I were your algebra to teacher. I would probably say mode is the best way to talk about it, cause I indicates that that the majority of the people make 20,000 and in the media and just tells you like what the middle person is, which still isn't a good representation of what's going on here. Okay, thank you very much.

Okay, So if Bloomberg BusinessWeek North Americans describe his study collected data from a sample of 28 2861 subscribers, 59% of the respondents indicated an annual income of 75 care arm or and 50% reported having an American Express credit card. So part they ask us for the population of interest in the study. And it's gonna be North American, um, subscribers. Oh, Business Week per piece, says his annual income. A categorical quantity variable. And it's gonna be quantitative because, um, income is a number and numbers are generally quantitative data, Parsi says. Um, it's ownership of American Express card, eh? Categorical or quantitative data? And this is gonna be I'm categorical because it's not a number involved. It's just Do you own a card or not? Purty. Does this study involve cross sectional Laurie Time? Siri's data and it's gonna be cross sectional because it was happened. It all happened at one time across a large area. If it was, if it happened over a long period of time in one area, then it would be time series E says. Describe any statistical inference is Bloomberg Business Week might make on the basis of the survey, and I'm just based on the data, we can see that most of the drivers appears having anyone come. Of 75 Claremore and half of subscribers appeared to have an American Express card. So to generally have 75 kids or more income and they tend to, they do tend to have in American Express card. So we have that in our Christmas card and a income greater than 75 k just based on the data that they give us.

Yeah. In this question, we want to estimate the average difference in the percentage of foreign revenue for tech companies and basic consumer product companies. After you've verified the mean and standard deviations for the two types of companies, we can plug these numbers into our confidence interval formula. And notice here I'll answer question D I'm using T. Star, the T distribution because this is quantitative data, and we do not know the population standard deviations. All we know are the sample standard deviations. Now I've plugged in my means, my standard deviations and my sample sizes, but Mighty Star, Our smallest sample sizes 16, which means our degrees of freedom is going to be 15. And we want an 85% confidence interval for degrees of freedom 15 and R. T. Star for that is 1.517 Yeah. And now I'll use my calculator. Find the difference in the means which is 1806. And then when I multiply 1.517 by this big square root here, we're going to get 5.42 is our margin of error. And when we add and subtract 5.42 from 18.06, it's going to give us a confidence interval from 12.64 up to 23.48. And what this means is that we are 85% confident. The average difference in the percentage of foreign revenue for the two types of companies is between these two numbers. And notice these two numbers are both positive. Which will tell us that our yeah. Mhm. Tech companies are most likely to have a higher percentage of foreign revenue than our basic consumer product companies. Okay. But


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