Where Am I Going Wrong with Some LSSBB Sample Text Questions?

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    Hi all

    I have been studying for the LSSBB exam and some questions I am struggling (attached). Any assistance in figuring out 1) if I am wrong and 2) why I am wrong would be appreciated:

    For Question 46)

    I was considering both B and D. For B I question if that miminum yield is taken from the 95% PI then I would expect a minimum yield of 50 units or so as opposed to 100. I also tried using the regression curve but had to fudge an offset for the 95% PI.

    For D when I plug 2 and 4 into the regression I have answers of 12 and 37, so ‘around 20 to 40’ isn’t particularly correct.

    For Question 49) I chose C,  I would have assumed that there are not limitations on the residuals as they form there own distribution, it would be correct to say MOST residuals are within 2 std devs of the mean.

    For question 52) I would have chosen B

    For Question 152) I answered C with working out in the file.

    For question 184) I did not have the Partial Z table but went off an internet one. I used (Upper-mean)/(st dev/sqrt(units)) and did the same for lower but they numbers made no sense. I am not sure what I am doing wrong here. I have included my output from Sigmaxl to assist but would still like some assistance on the manual calculations.

    For 209) I chose D as I assumed the alternate hypothesis is the one we are trying to prove.

    Any assistance is greatly appreciated.




    1. Questions-for-Isixsigma.docx
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    Robert Butler

    The phrasing of several of the questions is terrible…and there is one that is simply wrong.  Now that we have that out of the way my thoughts on the questions are as follows:

    Question 46: I would choose B.  When you lay a t-square over the plot there is no way the minimum at 6 is anywhere near 100. If they are claiming D is the correct answer then I don’t see how that’s possible.  “Between 2-4” means anything between those two numbers so you would look at the values from 2.01 to 3.99 and, depending on which line you choose (regression line, 95% CI on means, 95% CI on individuals) you can get a 20-40 range.

    As an aside- if you are going to ask questions like this you owe it to the people taking the test to provide a graph that has enough detail to permit an assessment of questions such as this one – If I ever made a presentation where the required level of detail with respect to output was 10 units my investigators would be really upset if I gave them a graph with a Y axis in increments of 50.

    Question 49: I would choose D.  If the residuals can be described by a linear regression then the residual pattern is telling you that you have some unknown/uncontrolled variable that is impacting your process in a non-random fashion.  The good books on regression analysis will typically show examples of residual plots where the plot is telling you that you have something else you need to consider.  The three most common examples are residuals forming a straight line, residuals forming a curvilinear line, and residuals forming a < or a > pattern.

    Question 52: Of the group of choices C is correct but the question is terrible – I’ve never had a case where a manager asked me for the average cost of an item rather the issue was always the cost per item which means you calculate the prediction error based on the CI for individuals.  What they are doing is using the CI on means.  Thus for 3 standard deviations (the industry norm) you would have 4060 + 3*98/sqrt(35) = 4060 + 49.7 = 4109.7.  Your choice is wrong because the issue is not the average cost, rather it is the maximum average cost and a maximum average of 4200 means you are going to have a fair percentage of the average product costs in excess of 4200 – how much would depend on the distribution of the cost means relative to some grand mean.

    Question 152: I agree, the answer is B.  Please understand that what I’m about to say is not meant to be condescending.  You need to carefully re-read the question – RTY is a function of …..What?

    Question 184:  Your equations shouldn’t have the sqrt of 360 in them – the problem states the process standard deviation is 2.2 therefore that is not s it is sigma.  The issue is this – for the first equation the Z value is 1 and for the second it is -.681.  If you look at a Z table you will find for Z = 1 the area under the curve coming in from -infinity is .8413. If you subtract this value from 1 you get the estimate for the percentage of the production that are in excess of 8.4 and that is 15.87% and 15.87% of 360 = 57.13 which rounds down to their answer.

    However, there is the issue of the product outside the lower bound. This is determined by your second equation where Z = -.681. The area under the curve coming in from – infinity to -.681 is .2483. This means the total percentage of off spec (above the upper limit and below the lower limit) is .1587 + .2483 = .4070 which means the total off spec is .4070 x 360 = 146.

    Question 209:  The null hypothesis is that the mean is less than or equal to $4200 therefore the alternate hypothesis is that the mean is greater than $4200.  All of the other verbiage in the problem has nothing to do with the statement of the null and alternative hypothesis so I would agree with E.

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