Stat 1000: Tips for Web Assign HW 08
Published: Wed, 03/30/11
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General Tips for Web Assign and JMP
When working with Web Assign, always enter the answer to one specific box and then click "Submit Answer" to confirm that is correct before you move on to another box. Do not enter several answers all at once in several boxes before you click "Submit Answer". You risk being marked wrong due to some typo or something.
For some strange reason, JMP 8 occasionally computes wrong answers even if you have copied and pasted your data correctly. I suggest that, if it is feasible, type the given data into your calculator (in Stat mode as shown in Appendix D of my book), and have your calculator compute the sample mean. Compare that answer with JMP's answer for the sample mean. If they are the same, everything is fine. If they are not the same, close JMP 8 and restart it, recopy and paste the data, and check again. Sometimes you have to do this 2 or 3 times before JMP finally works. If it is not feasible to use your calculator to compute the sample mean, have JMP do the question 2 or 3 times, being sure to restart JMP and recopy the data each time, and confirm that JMP gives you the same answer each time before risking entering the results into Web Assign.
If you are taking the course by distance/online (Section D01) click here to see your tips for HW 08.
Study Lesson 9 in my book, if you have it, to prepare for this topic.
First, be sure to note
whether a question gives you σ, the population standard deviation, or s, the
sample standard deviation. That dictates whether you will use z or t when
testing your hypothesis.
Question 1 is basic P-value stuff as taught in Lesson 9.
Questions 2 and 3 are a good run through of the 5 steps to test a hypothesis.
Question 4:
If you need to use JMP or Crunchit! to make a confidence interval.
Personally, I would use JMP. Select and copy the data. Click "New
Data Table", then select "Edit" then "Paste with Column Names". Now
select "Analyze", "Distribution" and highlight "radon" and click "Y,
Columns", then click OK. You are now looking at a histogram and stuff.
Click the red triangle next to "radon" then select "Confidence
Interval" from the drop-down list. Select "Other" to get a pop-up menu.
It probably already has 0.95 typed in (for 95% confidence interval),
but, if not, be sure to type in 0.95. Make sure you click the box saying "Use known Sigma".
Click "OK" and you will then get a pop-up menu to type in the sigma
value. I believe σ = 9 in your case. Click "OK" and JMP gives you the
Confidence Interval at the bottom of the printout.
If you want to use Crunchit! Copy the "http:..." stuff for the
link to the data (shown at the top in your web browser) then select
"Data" and "Load Data from URL". Paste the link into the box and make
sure the box saying "use first line as column names" is selected. Make sure you also click the drop-down menu next to "Delimiter" and select "whitespace". Now,
you should see the data given in two columns in your spreadsheet.
Select "Statistics", then select "Z tests", then select "One-sample". In the pop-up window, make sure you click "radon" in the "Variable" box to highlight it. Type
the given standard deviation into the box (again, σ = 9) and make sure
the slider is set at 95% confidence and click "OK". You now get a
printout showing, among other things, the 95% CI.
If you need to use JMP or Crunchit! to test a hypothesis. You
should already be in the output screen having done the confidence
interval in part (a). You are now looking at a histogram and stuff.
Click the red triangle next
to the variable and select "Test Mean" from the drop-down list. Enter in
the
mean from your null hypothesis and enter in the given standard
deviation. Click
"OK" and JMP gives you the hypothesis test at the bottom of the
printout. Look
at my questions 13 and 14 for examples of how to read this printout.
If you want to use Crunchit! You should already have the data pasted in from part (a).
Select "Statistics", then select "Z tests", then select "One-sample". In the pop-up window, make sure you click the appropriate variable ("radon") in
the "Variable" box to highlight it. Type the given standard deviation
into the box and type in the mean you are using in your null hypothesis. Be
sure you click whether you are doing a two-sided, upper-tailed (greater than) or
lower-tailed test (less than) or else you will not be given the correct
P-value. Click "OK". You now get a printout showing, among other things, the
test statistic and P-value.
In either case (JMP or Crunchit!), you can now select, copy and paste your
output to a file ready for upload as usual.
Question 5 is just more practise at the concepts involved in testing hypotheses. My questions 13, 14, and 15 may be of help here.
Look at my examples 8, 9 and 10 in
Lesson 9 to understand how to put bounds on a P-value if you are using t. BE
CAREFUL! In Web Assign, when you are entering the critical values and tail
area bounds into your boxes always put the smaller value in the left box
and the larger value in the right box because the "<" signs demand
that.
In question 7, you
are asked for the standard error of the sample mean, that is not the standard deviation. I discuss the Standard Error of the sample mean in
Lesson 8 of my book. Use the Stat mode in your calculator to enter the data and compute the mean, x-bar, and standard deviation, s, but the standard error of x-bar is s divided by the square root of n.
Note the margin of error of
any confidence interval is everything that comes after the +/- in the
appropriate formula.
Question 8:
This is a matched pairs
problem. Study my questions 19 and 20 in Lesson 9 to understand how to do
hypothesis tests for matched pairs.
To use JMP to do a matched
pairs test, copy and paste the data into New Data Table the usual way
then select "Analyze", "Matched Pairs". Highlight both columns of your matched
pairs data and click "Y, Paired Response" and click OK. You will then be given
all the numbers you need.
Be careful to note which way JMP is subtracting the pairs (it tells you in its printout).
For example, if JMP says it is computing A - B, but you are
specifically told to compute B - A, you can simply change the sign of
your test statistic to fix that. Which is to say, if A - B produces a
test statistic of t = -2.3, then B - A would produce a test statistic of
t = +2.3. Similarly, the value for x-bar, the mean of the differences,
would be the same but have the opposite sign. The sign of the standard
deviation of the differences never changes. Similarly, this
affects the signs of the lower and upper limits of the confidence
interval for the differences that JMP makes. If JMP gave you the
confidence interval for A - B, the confidence interval for B - A would
be the same numbers but the opposite signs. Also note that changing the
signs also changes the order of the limits. Which is to say, if the
Upper Limit used to be +5, change the sign to -5 and that will now be
the Lower Limit. Similarly, if the Lower Limit used to be +2, change
the sign to -2 and that will now be the Upper Limit.
If you want to use Crunchit! (and I wouldn't) copy the "http:..." stuff for the
link to the data (shown at the top in your web browser) then select "Data" and
"Load Data from URL". Paste the link into the box and make sure the box saying
"use first line as column names" is selected. Make sure you have selected
"whitespace" as the delimiter to separate your columns. Now click "Statistics",
"T tests", and "Paired". Highlight column 1 in the first box and column 2 in
the second box. Be sure to select the correct alternative hypothesis and set
the appropriate confidence level, then click OK to get your
printout.
After
using JMP or Crunchit! to do the problem, I also suggest you do it by
hand since a question like this is always a possible exam question.
However, by hand, the best you can do is put bounds on the P-value,
whereas Web Assign requires an exact P-value.
Question 9 is just more practise at the concepts in Lesson 9.
You will need to study Lessons 6 and 7 in my study book to prepare for this assignment.
Question 1:
If you are ever asked to decide if a particular situation is binomial or not, remember, to be binomial, four conditions must be satisfied:
(i) There must be a fixed number of trials, n.(ii) Each trial must be independent.(iii) Each trial can have only two possible outcomes, success or failure, and the probability of success on each trial must have a constant value, p.(iv) X, the number of successes, is a discrete random variable whereX = 0, 1, 2, ... n.
If you are solving a binomial problem, and they ask you to compute a mean and/or standard deviation, read carefully. Do they want the mean of X? or do they want the mean of p-hat, the sample proportion? Be sure to study the sections about the Distribution of X and the Distribution of p-hat in my Binomial Distribution lesson (Lesson 6 in my new edition, Lesson 7 in older editions). Take a look, especially, at question 10 of that lesson as a good run through of these concepts.
Questions that give you μ and σ are undoubtedly dealing with bell curves. Make sure you have studied my lesson on the Distribution of the Sample Mean (Lesson 7 in the new edition, Lesson 6 in older editions). Always be very careful to note, are they asking you for the probability of one individual value (X)?, or are they asking you for the probability of the average or mean of n values (x-bar, the sample mean)? If you are dealing with X, use the X standardizing formula. If you are dealing with x-bar, use the x-bar standardizing formula.
Also, note that you can only do probabilities for X in these cases if you are specifically told that X is normally distributed. Otherwise, there is no X-bell curve, and the probability is unknown. However, thanks to the Central Limit Theorem, we can always assume there is an x-bar bell curve (the sample mean is normally distributed), as long as n is large.
Question 3:
How big a sample size n do you need to reduce σ(x-bar), the standard deviation of x-bar, down to a certain amount? You can solve that by some algebra, but I suggest you just use trial and error. Try n = 10, for example, and see if that works. If not try n = 20 or something. Play the Price is Right Clock Game. Try higher n's, lower n's until you home in on the n that works. With a calculator, I contend you can arrive at the correct answer quite quickly. Those of you who feel comfortable with algebra are certainly welcome to solve the problem that way.
Note, in Question 3, parts (c) and (d), it appears you do not have enough info to solve the problem because they have not given you a value for μ, the population mean. That is because the actual value is irrelevant. If you ever come across a problem like this, pretend that μ = 0, and then be careful to draw a picture and shade the region they describe. Proceed to compute your z-score, etc. Try it again, but this time using μ = 10 and making the appropriate adjustments to your bell curve and shade the region. You will discover you get the exact same z-score. This works no matter what you use for μ. That's why the easiest choice is μ = 0.
Question 4:
Again, be sure to look at my question 10 in my Binomial Distribution lesson to understand how to approach this question.
Question 5 is just more of the same stuff from Lessons 6 and 7 in my book (different people get different questions).
Question 6 uses the Sampling Distribution simulator at Rice Virtual Lab in Statistics. Read Carefully. They first have you play around with it using a Normal Distribution. But, the actual questions they ask want you to use a "Skewed Distribution". Note that, in the top left corner, you are given the mean and standard deviation of the population (μ and σ). The various questions you are being asked are about the distribution of the sample mean. Compare the answers for the mean and standard deviation of x-bar that the applet is giving you (next to the third histogram) with the theoretical values you expect if you computed the mean and standard deviation of x-bar using the formulas I give you in Lesson 7 of my book. This applet is illustrating the same concepts I discuss in Figures 1 and 2 in Lesson 7.
The fact is, you can answer all the questions they ask without using the applet. Just use your formulas for the mean and standard deviation for x-bar.