Follow:
|
Midterm Exam Prep Seminar March 5
|
Don't have my book or audio? You can download a free sample of my book and audio lectures containing Lesson 1:
Did you read my tips on how to study and learn Stat 1000? If not, here is a link to those important suggestions: Did you read my Calculator Tips? If not, here is a link to those important suggestions: Study Lessons 4 and 5 in my study book (if you have it) to learn the concepts involved in Assignment 3. Don't start working on the assignment too soon. Study and learn the lesson first, and use the assignment to test your knowledge. Of course,
always seek out assistance from my book, your course notes, etc. if you ever hit a question you don't understand, but try not to be learning things as you do an assignment. Learn first, then put your learning to the test.
Of course, always seek out assistance from my book, your course notes, etc. if you ever hit a question you don't understand, but try not to be learning things as you do an assignment. Learn first, then put your learning to the
test.
To type in formulas you are using and to show your numbers subbed into the formulas you can click the Equation Editor button in the toolbar that looks like the Sigma Summation symbol (you have to click the "..." other options button to see the sigma formula input button. Then click the various buttons to make your fractions and enter the symbols. However, the Equation Editor is extremely slow and clunky. Personally, I
would never use it. Just type ordinary text explaining what you are doing if you think you should show some work.
Exception: Always do any JMP stuff open-book. Have my tips in front of you, and let me guide you step-by-step through any JMP stuff. JMP is just "busy" work. The sooner you get it done and can move on to productive things like understanding the concepts and interpreting the JMP outputs, the better off you will be.
Then again, since you never have to upload the JMP printouts, perhaps you might not even bother to do the JMP at all. Most questions can be answered by hand even when they told you to use JMP.
This question is very similar to my question 2 in Lesson 4.
In part (d) you will have to work backwards. Arbitrarily mark b as some random value on your horizontal axis. Then mark
the given left endpoint somewhere to the left of b on the axis. Shade the region between the given left endpoint and b. That rectangular shaded area is what they are describing. You are given the proportion which tells you the area of the shaded region. You also know the height of the shaded region (your answer from part (a)). So, you can establish what the width of the shaded region must be because you know the width times the
height equals the area. Then, you can establish what b must be knowing that Right - Left gives you the width.
For part (e), since quartiles split the distribution up into 25% sections, you need to slice this rectangle into 4 equal pieces. That is quite easy to do since it is a rectangle.
I strongly recommend you read my section in Lesson 4 about the Z Bell Curve Ladder and the X Bell Curve Ladder and make the ladder every single time you have a bell curve problem. Then climb up or down the rungs. Many
students are guilty of not thinking a problem through, and consequently looking at Table A too soon. The ladder trains you to focus on the fact that Table A deals with z scores and Left Areas, but your problem may be interested in something else.
You will be using Table A for much of
this assignment. Here is a link where you can download the table if you have not already done so:
This is very similar to my Lesson 4, question 5. Make sure you have done all of
those questions first and have confirmed by repeated attempts, that you can get them 100% correct every time before you attempt this question on the assignment.
IT IS IMPERATIVE THAT A STUDENT CAN CONSISTENTLY GET MY QUESTIONS 5 AND 6 CORRECT EVERY TIME WITHOUT EXCEPTION. BE HARD ON YOURSELF. Students who make mistakes on this stuff, and find themselves saying things like, "Oh, I forgot to subtract from 1; or, oh, I
didn't realize that was the right area," are just setting themselves up to get most of the exam questions wrong. Always use my bell curve ladders to help you focus on the problem and always draw a diagram to visualize the problem.
This is very similar to my Lesson 4, question 6. Make sure you have done all of those questions first and have confirmed by repeated attempts, that you can get them 100% correct every time before you attempt this question on the
assignment.
IT IS IMPERATIVE THAT A STUDENT CAN CONSISTENTLY GET MY QUESTIONS 5 AND 6 CORRECT EVERY TIME WITHOUT EXCEPTION. BE HARD ON YOURSELF. Students who make mistakes on this stuff, and find themselves saying things like, "Oh, I forgot to subtract from 1; or, oh, I didn't realize that was the right area," are just setting themselves up to get most of the exam questions wrong. Always use my bell curve ladders to help you
focus on the problem and always draw a diagram to visualize the problem.
In part (e), do note that it is b they want, not -b, so be sure to determine the value of the z-score on the right side of the region.
For part (f), note that I also do a percentile example in my question 7. As I say in my question 7, the 80th percentile, for example, is the z-score
that has 80% of the area to the left of that score.
Make sure you have studied all my X-Bell Curve problems (questions 9 to the end) in Lesson 4 before you attempt this question. Make sure you use the X-Bell Curve Ladder to help you work your way through each part of this
question.
You also need to know the 68-95-99.7 Rule taught earlier in my lesson (questions 3 and 4 in Lesson 4). But, only use this rule to solve part (e). Never use the 68-95-99.7 rule unless you are clearly told to do so!
Part (h) is all about z scores. The higher your z score in a normal distribution, the better you did relative to others. See my question 14 in
Lesson 4 for an example of this principle.
A normal quantile plot is a way of inspecting a sample to see if it comes from a normal distribution. This is done by first computing the mean and standard deviation of the sample. Then, using that mean and standard deviation, it computes the standardized z score for each
data value. You now have the orginal score, X, and its standardized z score, Z. It then makes a scatterplot of X vs Z. This is called a normal quantile plot. This quantile plot will always have a positive association (rising trend), but that trend may be either linear or nonlinear.
If a normal quantile plot looks linear, then it is reasonable to assume the data comes from a normal distribution. The stronger the
linearity, the stronger the evidence that the distribution is normal.
Hint: This particular data set looks strongly linear on a normal quantile plot.
I show you how to determine a Sample Space through the use of two-way tables if necessary in Lesson 5 of my book. Note that all you are asked for is the sample space in each part, so your answer would be something like this (don't forget to use those squiggly
brackets "{}").
For example, here is the sample space for the outcome of flipping a coin twice where H=heads and T=tails: {HH, HT, TH, HH}.
Don't state the probabilities! You are not asked for the probabilities. In fact, in many of the situations students will be given for this problem, it is impossible to know the probabilities. You are just asked for the sample space.
With cards,
focus on what you are asked to select. You don't have to list all 52 cards. Is it just the colour of the card you are interested in (Red or Black?, R or B). Is it the suit of the cards (C, D, H, S)?
In part (c), note that there are only three coins, one of each for G, S and C, and you are sampling without replacement until you get G. So, if your first selection is G, you stop. But, if you get S or C, you proceed
to make another selection. Your sample space will look something like this: {G, SG, CG, ...}
Although this question appears to be a 3-circle Venn diagram problem (similar to my Lesson 5, question 18), they have left key information out that renders it not worth the effort to try to make the diagram. You are better off just taking each question as it
comes and answering it directly.
Part (a) Note that every entry in a Venn diagram represents an outcome. For example, a typical 2-circle Venn has 4 entries (the number where the two circles intersect), the number in A but outside of B, the number in B but outside of A, and the number in the rectangle but outside of both A and B). Since there are 4 entries, there are 4 outcomes in the sample
space.
Here, even though we don't have enough information to fill in the Venn diagram easily, we can still picture this problem as a 3-circle Venn diagram. Count the number of distinct regions inside the rectangle of a 3-circle Venn to identify the number of outcomes in the sample space.
You can also use two-way tables to identify all the outcomes in the sample space (but those two-way tables cannot reliably solve the probability
because we cannot use the independence multiplication rule). Along the top list Jets fans (two columns: either Yes, you are a Jets fan, or No, you are not). Down the side, list Bombers fans (Yes or No). Then bring in the Goldeyes fans in a second table.
Part (b)
This problem is easily solved using the General Addition Rule formula for P(A or B) as given in Lesson 5 of my book. Just focus on Jets
and Bombers.
P(A or B) = P(A) + P(B) - P(A and B)
Part (c)
This too can be used using a little algebra and that General Addition Rule formula. Hint: Focus on Jets and Goldeyes.
Part (d)
Keep in mind things you have learned from part (c), again you can use the General Addition Rule formula to solve
this algebraically. Focus on Bombers and Goldeyes.
Part (e)Look at my similar question 16(d). For example, you are given P(J), Jets, and P(B), Bombers, and you have also been given P(J and B), Jets and Bombers. If these two are independent, P(J)*P(B) should match the given value for P(J and B). If it matches, they are independent. If
it does not match, they are dependent.
After having answered parts (b) to (d), you know all the things to check independence of each pair of sports fans.
Part (f)
At this point, you now should know the probabilities P(J), P(B), P(G), P(J and B), P(J and G), P(B and G), and P(J and B and G). So, take a moment to now fill in the entire 3-circle Venn diagram to assist you in
answering the remaining questions.
Recall, if A and B are disjoint (or mutally exclusive), the P(A and B) = 0. You already know what the relevant probabilities are to easily answer this question. Also, if any of these pairs are disjoint, their circles on the Venn diagram should not intersect at all.
Part (g)
This is easily answered by checking off all the relevant regions in your Venn diagram and
adding them up.
I think it is a good idea to use my "check-mark method" that I show you in my Venn diagrams section when dealing with AND or OR. In your sample space, check off all the outcomes that belong to A. Now go back and check off all the outcomes that belong to B. This might mean you are checking off the same outcome twice. - If you want A and B, add up all the probabilities that have been checked off
twice. (Those are the outcomes that belong to both A and B, as required.)
- If you want A or B, add up any probability that has at least one check mark. (Those are the outcomes that belong to at least one of A or B, as required.)
Part (h)
Again, this is easily answered from your Venn.
|
|
