CQE Exam Questions ANSWERED [10 questions from Statistics]

hey guys andy robertson here with cq academy and i'm really excited for today's video where what i'm going to do is i'm going to walk you through uh 10 questions from the statistics portion of the body of knowledge we're going to go through one question from each of the eight chapters within statistics i'm going to explain how to solve the problem how to recognize what type of problem it is you're solving how to look up the right equations that you need to use on the exam and and then obviously walk you through the process of working those equations and solving the problems and in the in the process of doing that i want to share a free resource with you i call this my free cheat sheet you can get it at cqe academy dot com free cheat sheet and what i've done is i've taken all of the equations in the cqe body of knowledge for statistics there's 165 equations i've taken all those and i've condensed them down into a single 10 page pdf that you can use to help prepare for the exam and then obviously you can use it on exam day to save you time a lot of people waste time flipping through their book looking up equations and maybe they don't find the right one because there's different equations i want to give you this free resource so that you're as prepared as possible and you you understand how to use the equations and you're ready on exam day all right the second free resource hangout stick around to the end where i share another link to another free resource where i'm going to give you a bunch more practice exams to help you prepare for the cq exam all right let's head over the computer and get started all right let's get into this okay so what i wanted to do is i wanted to make sure that as we talk about statistics we cover the entire cqe body of knowledge so if you go over to the body of knowledge which i'll link below in the description there's eight sections you can see them all here and i wanted to do 10 questions so i decided to do two questions from statistical decision making because that's a really big chapter as well as statistical process control because that's another big one and then as we go through this i don't just want to talk about how to work the equations but i want to teach you how to know what equations you need to use because the first step in solving any problem is is asking yourself okay what type of problem is this and then once you understand the problem that you've been given it's all about learning how to work the problem the other thing is i'm going to add time stamps here to all the different questions if you're good with standard deviation and you're good with probability and you're good with the normal distribution you can jump right into statistical decision making and you can see anova or linear regression and that way you can kind of pick and choose which ones you watch all right let's get into it okay so the first one this is very basic right we're here in collecting and summarizing data and on the cq exam you're almost guaranteed to get a question like standard deviation or variance so here's the question calculate the sample variance for the following data set now again the first step in solving any problem is identifying what type of problem it is and again if you want to get this free cheat sheet that i'm about to reference go to cqacademy.com free cheat sheet because here's what it looks like on the cheat sheet you're going to find in the very top section is going to be all about collecting and summarizing data and what you see here is there's four different potential equations that you might have to use to calculate either sample standard deviation or sample variance or the population variance or the population standard deviation now given that the the question actually says the word sample variance we know that this is the right equation to use so we're solving for s squared here's that equation and i want to show you how to calculate this in real life obviously we have excel we have minitab but on the cq exam you're going to need to know how to calculate this by hand and it all starts by calculating x bar we know what our x values are right 3 5 7 9 and 11 but to actually do this calculation the first thing we have to do is to calculate the sample mean value and that's basically the summation of our values 3 5 7 9 and 11 which sum up to 35 and then we divide by n and in this situation we have five data points so n is equal to 5 and our sample mean is equal to 7. now that we have the sample mean we can start putting together a table to do the calculations so the way this table works is i've got all my individual x values and now what i want to do is i want to compare that x value against the sample mean so this should be the sample mean i don't know why it always gets cut off like that but essentially what i'm doing is i'm comparing every individual value against the sample mean so 3 minus 7 is negative 4 5 minus 7 is negative 2 7 minus 7 is 0 and so on and so forth and then the next step in the operation is to square it so before we take the sum we're going to square it so if we take these values negative 4 squared is 16 2 squared is 4 and so on and so forth we can basically sum up these squared values so if we do that the sum of these differences squared is equal to 40. and now we can basically plug that back into the equation to start calculating the sample variance so again we have 40 and we're dividing by n minus one so that's five minus one and our sample variance is 40 divided by four which is equal to 10. if you got 8.0 that means you likely calculated the population variance and you forgot to divide by n minus one you just divided by n which is which is five so 40 divided by five is eight and then if you took the square root of your calculation you you calculated the the standard deviation which are these two answers so 10 so 10 here is the right answer all right let's move on to the next one okay so you're preparing for an upcoming production run where the likelihood of of a defect a let's say we've got two defects so the likelihood of defect a is known to be seven percent and the likelihood of defect b is equal to four percent and there's an overlapping two percent of the population that has both defect a and defect b all right so both of these defects can be reworked simultaneously what is the total percentage of product that should be planned to be reworked again right the first step in any problem is understanding what type of problem we're trying to solve and when we talk about probability right we can go again to our cheat sheet and we can we can talk about is this an or equation or an and equation and because we're trying to find the total percentage of defective products it's going to be an or situation because we're going to have to rework a product if it has defect a or defect b or if it has both so let's talk a little bit about how to calculate that that probability so when we're calculating the union of two events that are not mutually exclusive the way we calculate that is the probability of a plus the probability of b minus the intersection of a and b so we know that a has a probability of seven percent b has a probability of four and that two percent of the population has both a and b all right so we can basically plug in what we know and calculate the answer to be nine percent we take seven plus four minus two is nine percent now i wanna graphically show you what this looks like because this might be a little bit confusing so this is this is a picture that i like to use that represents the union of two events that are not mutually exclusive so over here on the left we have event a or defect a and that's seven percent and on the right here we have defect b and like the problem statement said is that there's an intersection between these two events where two percent of our population has both defect a and defect b and the probability that we're trying to calculate is it can be visually thought of as like this area here shaded in blue and when we calculate that area we take a plus b minus the intersection because essentially when there's an intersection we don't want to double count those defects so nine percent of our total product produced will have either defect a or defect b all right probability so a shipping operation distributes product or ships product at a mean time of 48 hours from the receipt of an order they get an order 48 hours later they ship it out right maybe that's your standard amazon two-day delivery and there's a standard deviation of approximately six hours of shipping what percentage of shipments go out between 42 and 54 hours now we can answer this question but i want to help you visually understand and and visualize what what's going on here in the problem imagine a normal distribution here with a mean of 48 hours and a standard deviation of 6. what the question is asking is what is the area under the curve from 42 hours to 54 hours and you can see what that looks like here i've shaded that in green visually so you can see what part of the distribution represents that period of time and the way we calculate probability using the normal distribution is with something called the z transformation so again if you go to your your exam day cheat sheet you can find this z transformation here to help you calculate the cumulative probability of the normal distribution so so let's let's do some some transforming so the first transformation is we're going to transform 42 hours which is this data point x into a z score so 42 minus 48 that's our mean value divided by 6 is a z score of minus 1. so essentially we've transformed this x value of 42 hours into a z-score of minus one we can do the same thing with an x-value of 54 hours we can transform that into a z-score so 54 minus 48 is 6 divided by 6 is is positive 1. and of course you can see that over here right we transform this x value into a z score and now that we have these z scores we can translate this into a probability score this is a normal probability table and the way this thing works is you start here on the vertical axis this is the actual z value the ones place in the tens place and then across the top is the hundreds place and essentially what we're looking for is the intersection of of z of 1.00 which happens to be 0.34 now let me show you what this looks like graphically so the way this table works is that number that you saw that 0.34 represents the area under the distribution from the mean value to our z-score so from from the mean to z equals negative one is 34.13 and then on the right side from our mean value to our positive one z-score is another 34 and cumulatively if we go from z equals minus one to z equals positive one we're capturing 68 of the distribution which is the answer to the question 68 of our shipments go out from 42 hours to 54 hours from the time of receipt that's how you solve a probability equation using the normal distribution all right let's keep going so statistical decision making you know i honestly feel like it's kind of cheating a little bit to give you the the type of question right remember when you're on the cq exam or or if you're in real life you're going to be given a problem statement and you don't know what type of problem it is so remember the first step in solving the problem is reading the problem understanding the context clues and the variables that you've been given mean value is 6.75 so we know x bar and we also know the population standard deviation is known and it's 0.75 inches we also know that that our sample size is 60 units so we've sampled 60 units and we know we want to calculate the 95 confidence interval so here it's pretty easy right the question tells you what type of question it is we want to know the confidence interval the 95 confidence interval so we have all of our variables here so again we can use that that free cheat sheet to look up the right equation associated with a confidence interval and remember we're looking to calculate a confidence interval for the population mean we know our sample mean of 6.75 and we're trying to create an interval estimate of the population mean so when we go here to our exam day guide there's actually two different equations that you can use to create a confidence interval for the population mean and it all depends on what you know so there's this column over here called use when so for example we use this equation here when the population variance is known which we do know and the sample size is greater than 30. so let's take this equation x bar plus or minus a z score times the standard deviation divided by the square root of n and let's plug in our variables now and calculate the confidence interval so we know the sample mean 6.75 and then the z-score so this is the only piece of information that we don't yet have and essentially what we have to do is we have to translate this alpha risk into a z-score now instead of doing that for you here and showing you all that what i'm going to refer you back to is a whole different youtube video that i created on confidence intervals to show you the math behind why this equation is what it is and and understanding the sample mean distribution and these critical z-scores i'll link that in the description below but go check that out the alpha risk of five percent translates into a z-score 1.96 and we we can calculate our interval estimate to be 6.75 plus or minus that should be a minus there 0.189 all right so let's keep going here in statistical decision making and let's talk about an anova table so we have a one-way anova analysis and we have 10 treatment groups and a total degrees of freedom of 19. what we have to do now the problem statement is calculate the f value for this anova table let me show you how to do that now before we get into the actual math i want to again go back to our cheat sheet here and talk about how you can use the cheat sheet to answer these questions so the first thing is let's start with the end in mind the f value is calculated as the mean square of the treatment divided by the mean square of the error so we're going to have to calculate these two things and the way we calculate the mean square is to divide the sum of squares by the degrees of freedom so we'll do that for both the treatment and the error and of course to do that we're going to have to calculate our degrees of freedom for the treatment and the total degrees of freedom and we're going to have to calculate the sum of the squares so let me walk you through now how to do that okay so the first things first is the the treatment sum of squares so we need to calculate the sum of squares of the treatment and we can do that using this equation here so the total sum of squares is equal to the sum of squares of the treatment plus the sum of squares of the error we know that the total sum of squares is equal to 100 that's right here and that's also equal to the sum of squares of the treatment plus 55 which is the sum of square the error and that translates to 45. we know the sum of squares of treatment is equal to 45 45 plus 55 equals 100. we can do the same thing for the degrees of freedom the problem statement tells us that we have 10 treatment groups so what is the degrees of freedom of the treatment well that's equal to a minus 1 where a is the number of treatment groups so we've got 10 minus 1 and the degrees of freedom of the treatment is equal to 9. and now that we have that information we can calculate the degrees of freedom of the error we know that in total the total degrees of freedom is equal to the degrees of freedom of the air plus the degrees of freedom of the treatment so we know that 19 is equal to the degrees of freedom of the air plus 9. we can essentially rearrange this equation and calculate the degrees of freedom of the error to be 10 and now we're ready to calculate the mean squares so the mean square of the treatment here is the sum of squares of the treatment divided by the degrees of freedom of the treatment so we take our sum of squares 45 divide by 9 which is our degrees of freedom and we know that our mean square the treatment is equal to 5.0 we can do the same thing for the mean square of the error we can take the sum of squares of the error 55 divide by the degrees of freedom of the error of 10 and get a mean square of the error of 5.5 and now that we have those two pieces of information we can finally calculate our f statistic which is simply just the ratio of these two variances mean square the treatment divided by the mean square of the error and that comes out to an f statistic or an f value of 0.909 giving us the right answer now the next step if you're a quality engineer or a green belt or black belt is to take this f statistic compare it against a critical f value and then make a conclusion regarding this anova table in this analysis to determine whether we can reject the null hypothesis or fail to reject it all right let's keep going here now we're talking about relationships between variables so let's say we've got a problem on the cq exam or the green belt exam and we've created a linear regression model and our data has the following values so s y y is 31 s x y is 12 and s x x is equal to 76 this is your standard linear regression problem and the question is what percentage of the variation in y can be explained by the variation in x and again i feel like it's cheating because at the top of these slides i'm putting relationship between variables but even as you read the problem and you see words like linear regression or you see parameters like x y y and s x y those should be the things that tip you off as to okay this is a linear regression equation and i need to go to my exam day cheat sheet and i need to look at my correlation coefficient or linear regression equations so if we go to the cheat sheet there's two types of parameters there's the pearson correlation coefficient and the coefficient of determination and if we read these and we're familiar with them right we know that the coefficient of determination or r squared reflects the percentage or the proportion of the total variation in y that can be explained by the variation in x so obviously to calculate r squared we have to calculate r so we can calculate r we we have s x y divided by the square root of x x x times the square root of s y y and we can plug in our variables here 31 12 and 76 and calculate an r value of 0.25 now all we have to do to calculate our coefficient of determination is to simply square that so 0.25 squared is equal to 0.06 and basically the conclusion is that 6 of the variation in y can be explained by the variation in x and to obviously to help you visualize that i want to show you this picture these are some common scatter plots and their associated r values so so for example this one's pretty close to ours and you can see that there is some some low positive correlation right as as x increases y tends to increase as well but but not much of that variation can be explained only by x right there's got to be some other independent factor out there that that is causing some variation in in our response all right spc let's get into this okay so you're manufacturing some widget and you're using an x bar and r chart to control a critical feature on the product and you've measured you you know your grand mean your x double bar you know r bar and you know your subgroup sample size of eight identify or calculate the upper control limit for x bar okay so again let's go back to our exam day cheat sheet we've got a whole section on spc this is the x bar in our chart and really the equation that we have to complete here is the upper control limit for x bar is equal to x double bar plus a2 times r bar now the only thing we don't have or the only thing we don't know is the a2 factor so again on the cqe exam you're going to have to look up this a2 factor and you can use your exam bay cheat sheet so we know our subgroup sample size of 8 and we can simply get our a2 factor of 0.373 okay so i've added that up here to to our known variables and then i've repeated that equation and let's start filling in what we know 225 plus that a2 factor times 12 is an upper control limit of 229.48 all right let's keep going so let's stay here in spc but obviously let's move on to the attribute data control chart of the p chart so let's read our statement what is the upper control limit for a p chart when the average daily inspection quantity is 50 and the historical percentage of defective units is 0.05 or 5 percent again right we just want to start by saying what type of problem is this and it's pretty clear in the problem statement that that this is a a spc question on on the p chart so we go to our exam day guide we look up the p chart equations we know what the upper control limit calculation is and based on the problem statement we know that n bar is the average daily inspection quantity right this is the average sample size that's 50 units per day and on average the average number of defects that we experience is 0.05 or 5 and we can essentially plug those two variables back into this equation and solve for that upper control limit so it's about 14 now i want to i want to share something specific about the p chart if you look at this chart here obviously you can see the the percentage right the percentage of defective items trending daily but you'll also notice that the upper and lower control limits can change so in this particular problem we used nbar which is the average number of daily units inspected but your daily number of units inspected can change from subgroup to subgroup maybe on this particular day we inspect 100 units or 200 units or 30 units you can calculate a unique control limit using that n value as opposed to the n bar value or the average daily units inspected all right let's keep going into process capability this is section seven in the body of knowledge so again the parameters and the problem statement are fairly obvious here calculate cpk using the following parameters so we have an upper spec limit a lower spec a population standard deviation and a population mean now again to help you answer this question or to help you understand process capability i really want you to be able to visualize it so here's that exam day guide we understand the equation we need to use let's kind of throw that up on the screen and basically we can start plugging in the values so the upper spec is 205 minus the mean of 190 divided by 3 times s now in this particular equation we have s which is the sample standard deviation in this particular example we know the population standard deviation it's it's really all the same so plug that in here as as the variation on the bottom and then we can calculate the lower side so 190 minus 145 divided by 3 times our sigma value of 10 and then basically we're looking for the minimum value between upper and lower and if we keep running this out we can calculate our process capability to be 0.5 which quite frankly is not that good and i want to help you visualize this and again just kind of understand process capability more deeply so here's our distribution we have a mean value of 190 and a standard deviation of 10 and if we overlay our specification limits you can see that we're not centered between the spec limits and basically what that means is everything in green here is going to be conforming to the specification and then everything in red here is going to be out of spec and that correlates with our our cpk value because we're going to produce a lot of non-conforming products and you can see here on the lower side of the distribution that should say lower spec we're four and a half standard deviations away from the lower spec and on the right side we're only one and a half standard deviations away which again explains that cpk value because we're pretty close to the mean here now if we were to shift our distribution if we could center up our process around a mean value of 175 we'd be three standard deviations away on both sides and our cpk value would go from 0.5 to 1.0 all right let's keep going last but certainly not least design of experiments so here's the question you've performed a full factorial doe to improve the yield of a process so the response here is yield and we have two factors at two levels we've got a high and a low for factor a and factor b and we've measured the following responses you can see here that as we go from high to low and we we vary our different factors are you can see that our yield is changing and we have four treatment groups now how do we calculate or how do we estimate the effect associated with factor b again we can we can go to our exam day guide we can find the the doe portion of that exam day guide and we can find this equation down here so this is how we estimate the effect of any particular factor in an experiment so let's let's see what this looks like in real life so here's that equation we want the average at the highs minus the average at the lows so what so what does that mean how do we do that so for factor b specifically the first two treatments have b have factor b at a high and so what we do is we take the average value of 64 and 75 and then we have to take the difference of that against the average at the lows so for example for factor b where we have lows in treatment groups 3 and 4 and those have yields of 87 and 95 and then if we just kind of play this out what we find is that as we vary factor b from high to low our yield actually improves by 21.5 percent from high to low right so that's the estimated effect of factor b which is pretty substantial for for yields to change by 20 that is a big deal all right that was it again i wanted to wrap up with those two free giveaways so if you're preparing for the cqe exam go sign up and get this this free guide this free cheat sheet it has all 165 equations from the statistics section of the body of knowledge and that way when you take the exam you are as prepared as possible you have the best resources and you're going to manage your time wisely because you have a very uh condensed version of this cheat sheet to really help you be successful and then free practice exams i'm a huge believer in practice exams go to cqecademy.com free practice exams to get more of those i've got statistics practice exams i've got all sorts of other free press exams that you can get for free and again start practicing and getting ready for the exam all right that was it i hope you enjoyed it i've got a bunch of links in the description below if you really loved this and you thought it was valuable hit that like button that way i know to continue creating content just like this and if you want to stay on this journey to become a cqe and pass that exam hit that subscribe button and that bell icon so that as i publish new content you get notified and you keep learning and growing and pass the exam alright thanks so much

Channel: CQE Academy

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Keywords: CQE Exam preparation, CQE Exam Questions, CQE Certification, CQE Training, CQE Exam Training, CQE Exam Certification, CQE Exam, ASQ CQE Exam Preparation, ASQ CQE Exam Questions, ASQ CQE Exam, CQE Preparation Material, ASQ CQE Training, ASQ CQE online course

Id: s5Q-6Yv-08I

Length: 27min 3sec (1623 seconds)

Published: Wed Jun 09 2021