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Final Exam Prep Seminar
Sunday, April 12
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$40, pay at the door
Sunday, April 12
9:00 am to 6:00pm Room 100, St. Paul's College, UM campus
Have you tried my Audio Lectures?
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Don't have my book or audio lectures? You can download a free sample of my book and audio lectures containing Lesson 1:
Tips you may have missed:
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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:
You need to continue studying Lesson 8: Confidence Intervals for the Mean and Lesson 9: Hypothesis Testing for the Mean. You also need to study Lesson 10: Inferences for Two Means (only in newer editions of Grant's Tutoring
Basic Stats 1) and Lesson 11: Inferences about Proportions (formerly Lesson 10 if you have an older edition).
IMPORTANT NOTE:
Only study to the end of question 2 in Lesson 10 of my book. The rest of Lesson 10 is now OMITTED from the course. Which is to say, you need to learn how to do
confidence intervals and hypothesis tests for matched pairs , but you do not need to learn how to do confidence intervals or hypothesis tests for two-sample problems.
You will be using Table A and Table D while doing this assignment and learning these lessons. Here is a link where you can download those tables if you have not done so already:
Remember: When listing your givens make sure you distinguish between being given the population standard deviation, σ, and the sample standard deviation, s. You can use z for an inference for the mean if and only if you are given sigma.
Exception: We
always use z for proportion confidence intervals and hypothesis tests, never t.
Important Note: Unlike what I instruct in my book, make sure that you compute a P-value every single time that you perform a hypothesis test. They have decided to not teach about critical values this term, so there is no need to use Table D to get z* or t*, the critical value, for any hypothesis test.
Because you are not using critical values, it therefore becomes essential to compute a P-value.
Your steps to test a hypothesis should always be:
- State the Hypotheses and so establish whether the test is upper-tailed, lower-tailed, or two-tailed.
- State the given level of significance, alpha. Let alpha =
5% if none is given.
- Compute the test statistic using the correct formula for z or t.
- Compute the P-value by marking the test statistic on a bell curve and shading the appropriate region according to your alternative hypothesis.
- State your conclusion knowing that you always reject Ho if the P-value < alpha.
A Warning about StatsPortal
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Make sure that you are using Firefox for your browser. Don't even use Internet Explorer. It actually also has some glitches in the HTML editor boxes.
Do note that every time you exit a question in StatsPortal, the next time you return to it, the data may very well
change. Do not press the "back-up" button on your browser in a question. That, too, will change the data. When you are prepared to actually do a question, open the link, keep it open, and do not close it until you have submitted your answers. Be sure to press "Save Answers" once you have done any calculations and entered any information to ensure the data does not change and force you to start over again.
After you submit the answer to a question, if you
have been marked wrong on any parts, be sure that you write down the correct answers before you exit the screen (or grab a screen shot). To try a second attempt at the question do not click the link to the question again, that will change the data and you will have to start all over again. Also, DO NOT click "try again" or make a "second attempt." That will also reset the data.
Instead, exit back to the home screen where they show the links for
all the different questions on the assignment. Where it shows the tries for a question on the right side of your screen, you should see the "1" grayed out, showing that you have had 1 attempt. Click the number "2" to get your second attempt with the same data. That way you can enter the answers you already know are correct and focus on correcting your mistakes.
You should also have already downloaded the JMP statistical software which was provided with
either one of the course options for StatsPortal as mentioned in your course outline.
Make sure you have gone through Assignment 0 completely to learn how to use the interface. I also suggest you print out a copy of question 8 in Assignment 0 (Long Answer Questions - Part 3) so that you have the steps for saving and uploading files into the HTML editor in front of you.
A general note about inputting your answers
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- When they request a confidence interval, you are always provided with two boxes. Be sure to put the lower limit in the first box, and the upper limit in the second box. Which is to say, always subtract the margin of error first, to
get your lower limit. Then add the margin of error to get the upper limit.
- When they request a P-value in a problem where you are using t, you are always provided with two boxes. Be sure to put the lower limit in the first box, and the upper limit in the second box. Which is to say, when you find the bounds on Table D, if you are reading from left to right, you are going to get the larger
bound first (for example you may find the upper tails are between 0.05 and 0.025). Reverse this order, to put the lower bound in the first box. So, in my example, you would say the P-value is between 0.025 and 0.05.
- Did you get a t test statistic that is off the charts? If your t is so small that it is off the left side of the table, then say your upper tail is between 0.25 and 0.50 (don't forget
to double these bounds if your test is two-tailed!). If your t is so large that it is off the right side of the table, then say your P-value is between 0 and 0.0005 (don't forget to double these bounds if your test is two-tailed!).
Question 1: Confidence Interval and Hypothesis Test - Carbon Monoxide
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Be sure to read my tips above for inputting confidence intervals and P-values!
You need to decide whether to use z or t to construct the confidence interval for the mean, and test the hypothesis for the mean in this question. Otherwise this a
standard confidence interval and hypothesis test question.
Remember: if you are given the POPULATION standard deviation, sigma, you can use z. Otherwise, you must use t.
BE SURE TO USE THE GIVEN VALUES FOR THE MEAN AND STANDARD DEVIATION IN YOUR CALCULATIONS. Do not compute the values yourself using the stat mode in your calculator. (You can do that as a check, if
you wish, but it is important that you use the rounded off values they give you.)
To use JMP for this question: First, open a New Data Table, name your column CO Level and enter the data down that column.
Select "Analyze, Distribution" and make "CO Level " the "Y Column "
and click OK to get the Histogram and stuff. Click the red triangle next to the variable and select "Test Mean" from the drop-down list. Enter in the mean, mu, from your null hypothesis in part (c) (the information for the hypotheses was given in the orginal paragraph; I believe it is 5.0). Click "OK" and JMP gives you the hypothesis test at the bottom of the printout. Look at my questions 16 and 17 for examples of how to read this
printout.
Remember: Prob > 't' is the two-tailed P-value Prob > t is the upper-tailed P-value Prob < t is the lower-tailed P-value
JMP does not know the alternative hypothesis, so it gives you three choices for the P-value. You should know which is correct. JMP also tells you the value of the test
statistic in the "Test Mean" output which you can use to check your calculations for part (d).
You can also use JMP to construct the confidence interval for you, but they asked you to do it by hand. Perhaps use JMP to check your answer though.
Click the red triangle next to CO Level above your histogram and select "Confidence Interval". Select
"Other" to get a pop-up menu. Type in your desired level of confidence as a 2-decimal place value. It probably has 0.95 typed in (for 95% confidence interval). Click "OK" and you will then get the confidence interval added to your printout. This interval should match the answer you got in part (a).
Question 2: Confidence Interval and Hypothesis Test - Grocery Expenses
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Be sure to read my tips above for inputting confidence intervals and P-values!
Much like question 1, just no JMP this time. In part (e), you are expected to type fail to reject or reject in the box
as is appropriate.
For part (f), keep in mind the concept I introduced in Lesson 9, question 13(d).
Question 3: One sample t Test and Matched Pairs - Reaction Times
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Note that parts (a) - (c) are focusing just on the right-handed reaction time, so be sure to use the given sample mean and standard deviation for the right-handed times in the Right row.
Parts (d) - (i)
are now focusing on the matched pairs problem. Make sure you have studied questions 1 and 2 in Lesson 10 before you attempt these parts.
Note that the A and B scores in a particular matched pair are dependent, not independent. However, each pair is independent of other pairs. Put another way, the B score depends on the A score if you have a
matched pair, but each pair is independent of any other pair.
As always, if a sample size is small, other methods are only reliable if the population is normal. In the case of matched pairs, if the sample size is small (less than 15), the differences must be normally distributed.
Question 4: Matched Pairs - Ages of Married Couples
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As they clearly say, this is another matched pairs problem, so note that it is the Difference (H-W) that gives you the relevant information. You are asked "whether husbands are older than wives on average." That should make it clear what the
hypotheses will be.
Again, questions 1 and 2 in Lesson 10 are relevant examples in my book.
Question 5: Sample Size for Proportions |
They give you an unusual level of confidence so you will have to read Table A backwards to get the z*. Read Lesson 8, question 10 for an example of how to do this properly.
This uses the sample size formula for
proportions as taught in questions 5 and 6 in Lesson 11 of my book.
You now have TWO sample size formulas! One is for MEANS (Lesson 8, questions 6 to 8) and the other is for PROPORTIONS (Lesson 11, questions 5 and 6). One needs a sigma, one does not.
Cheesy trick to help tell them apart:
- If
they give you sigma, the population standard deviation, they must want you to use the sample size formula for means because that formula needs a sigma. Read the question, they will clearly tell you that you are trying to estimate the mean.
- If they don't give you sigma, then they can't be trying to estimate the mean (because you have to be given a sigma for those questions). They must be estimating a proportion. Use the sample size
formula for proportions. It doesn't need a sigma.
In part (c), they merely want to know what the squared value is. So, if that want the margin of error to be a tenth the size, you would require 100 times the sample size. You would just type 100 in the box.
Don't use the sample size formula in part (d)! It will be too good an answer, possibly.
They want you to use the inverse-square relationship. Divide the old margin of error given in part (a) by the new margin of error given in part (d) and square it. Then multiply that by your answer for the sample size in part (a).
Don't forget your Paint-Can Principle when stating the answer for n. I wouldn't worry about this
question. In general, if they really want you to use the Inverse-Square Relationship, they will give you much more obvious changes to the margin of error (like doubling it, or something).
Part (e) is back to using the sample size formula again, but this time you have been given a value to use for p*.
Question 6: Inference for Proportions - Senate Scandal |
Clearly, this is hypothesis testing for proportions. Study Lesson 11 in my book. Especially questions 2 and 3. Note the word "majority" as discussed in question 3 of my
Lesson 11. A majority means p is more than 50%.
BE CAREFUL WHEN COMPUTING Z SCORES ON YOUR CALCULATOR FOR PROPORTIONS!
Students frequently get marked wrong even though they are doing things correctly because they are rounding off too much during their calculations. I suggest you round off to no less than 5 decimal places during your calculations for z. Better yet, don't round off
at all, use the memory function in your calculator.
Here are some tips:
- If p^ = x/n gives a messy decimal, round it off to 5 decimal places for safety, no less. Better yet, just leave it as a fraction and type it into your calculator as is.
- Compute the entire standard deviation of p^ in one step on your calculator and, preferably, store the answer in memory. If you don't know how to use memory, record the answer to no less
than 5 decimal places.
Example:
Let's say n= 345 and p= 0.40 and p^ = x/n = 123/345.
- I compute p^ = 123/345 = 0.35652 rounded off to 5 decimal places. But, since it is a mess, i will keep it as 123/345 in my calculations.
- To compute z:
- The denominator is square root of [p(1-p)/n]. You can do this all in one step on your calculator. To square root everything, press square
root then press the open bracket button on your calculator. Never close that bracket! There is no need, and you risk closing it too soon. Then just type everything in as the formula prescribes brackets and all.
- So, my p=0.40 and my n=345.
- Calculator: square root, open bracket, 0.40 times, open another bracket, 1 subtract
0.40 close bracket, divide 345 equals
- You should get 0.026375...
- Store this result in memory (check your calculator manual or google the calculator manual), or write it down to at least 5 decimal places.
- Now compute the top, p^ - p and divide it by the bottom.
- So, my p^ = 123/345.
- Calculator: 123 divide 345 subtract 0.40
equals
- You should have -0.043478... on your screen, but keep going:
- divide, recall memory (to recall the bottom calculation you did earlier; or, if not using memory, divide 0.026375) equals -1.648...
- Always round z to 2 decimal places, so z= -1.65.
Question 7: Inference for Proportions - Conservative Support
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Much the same as the previous question except this time they have clearly given you the value of p to use in your hypotheses.
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