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Final Exam Prep Seminar Scheduled
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The Final Exam Seminar will be Friday, December 5 from 9:00 am to 6:00 pm, and will be held on the UM campus (room 100 St. Paul's College).
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.
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. Don't have my book? You can download a free sample of my book and audio lectures containing Lesson 1:
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.
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.
To use JMP for this question:
First, open a New Data Table, name your column "Radon Level" and enter the data down that
column.
Select "Analyze, Distribution" and make "Radon 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) (I believe you are told it is 200). 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).
By the way, you could 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 Radon 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).
Good practice at test statistics and whether you should use z or t.
Much like question 1, just no JMP this time. In part (d), you are expected to type fail to reject or reject in the box as is appropriate.
As they make quite obvious, this is a matched pairs problem. Be sure to study questions 1 and 2 in Lesson 10 of my book. If you have an old edition of my book, matched pairs may be taught at the end of Lesson 9, questions 19 and
20.
Note that the A and B scores in a matched pair are dependent, not independent. However, each pair is independent of other pairs.
For part (f), keep in mind the concept I introduced in Lesson 9, question 13(d).
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.
Note that part (c) is talking about the Inverse-Square Relationship for sample size which I introduced in
Lesson 8, question 8. They don't want to know n, they want to know what multiplier or divider would be used.
Here is another way to think about the Inverse-Square Relationship. Essentially, if you want your margin of error to get smaller, then you want your sample size to get larger by the square of the factor. If you want your margin of error to get larger, then you want
your sample size to get smaller by the square of the factor.
- This means, if you want to multiply the margin of error, you divide the sample size.
- If you want to divide the margin of error, you multiply the sample size.
For example, if I want to divide my margin of error by a factor of 7, then I multiply my sample size by a factor of 49
(7-squared). If I want to multiply my margin of error by a factor of 5, then I divide my sample size by a factor of 25 (5-squared).
In part (c), they merely want to know what the squared value is. So, if that want to increase the margin of error 7 times, you would reduce it by a factor of 49.
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. That tells you how much to multiply your answer for the sample size in part (a) by. 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 with an unusual level of confidence. Recall my Lesson 8, question 10 for an example of getting z* for an unusual level of confidence.
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.
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