Stat 1000: Tips for Assignment 5
Published: Sat, 03/31/12
Did you miss my Tips on How to Do Well in this Course? Click here
Did you miss my Tips for Assignment 4? Click here
If you are taking the course by Distance/Online (Sections D01, D02, etc.), click here for my tips for your Assignment 5.
If you are taking the course by classroom lecture (Sections A01, A02, etc.), click here for my tips for your Assignment 5.
Study Lesson 8: Confidence Intervals for the Mean and Lesson 9: Hypothesis Testing for the Mean in my book, if you have it, to prepare for this topic.
You will be using Table A and Table D while learning Lesson 8 and 9
and doing this assignment. Here is a link where you can download those
tables if you have not done so already:
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 making your confidence interval or testing your hypothesis.
Question 1
is standard confidence interval for the mean stuff. Make sure you properly interpret the confidence interval. Look at my question 1(b) in Lesson 8 for an example of that. Also take a look at question 10 in the same lesson for an example of how to deal with an unusual level of confidence.
Question 2 is using the sample size formula introduced before question 6 in my Lesson 8. Be careful in part (d). You may want to take a look at my question 2 in Lesson 7 as an illustration of the concept they are discussing.
Question 3 requires some challenging algebra. Take a look at my question 13(c) in Lesson 9 as a starting point for this question. So you can determine what the sample mean, x-bar, must have been. You know that the Upper Limit, UL, of the confidence interval (given) must equal the sample mean + z* times Sigma(x-bar). You can compute Sigma(x-bar) since you were given both sigma and n.
UL = x-bar + z* Sigma(x-bar).
Sub in all you know, and that leaves z* as the only unknown. Isolate z* algebraically to solve it. I think you will discover your answer for z* is not on Table D, so you won't be able to establish the level of confidence that way. But, remember that the level of confidence is the area between z* and -z* on the bell curve, so you can figure out that percentage from Table A.
Question 4 is good practise at confidence intervals and hypothesis testing for the mean. Part (d) is referring to the concept I discuss in question 13(d) of Lesson 9.
Question 5 is much like question 4, except with an unusual level of confidence. Because the level of significance in part (b) is unusual and not on Table D, skip Step 2 in my steps for hypothesis testing. You won't need it anyway, since you have to compute the P-value anyway.
Question 6 is another runthrough of hypothesis
testing. Be sure to read the section in Lesson 8 about "Inferences for
the Mean are robust" that I write in the pages leading up to question 1
to understand what they are getting at in part (b).
To use JMP, click "New Data Table", then enter the data into
Column 1. Double-click Column 1 and name it something appropriate, like
"Wait Time". Now select "Analyze",
"Distribution" and highlight "Wait Time" and click "Y, Columns", then
click
OK. You are now looking at a histogram and stuff.
To test the hypothesis. Click the red
triangle next to "Wait Time" then select "Test Mean" from the
drop-down list. Enter in
the
mean from your null hypothesis and enter in the given standard
deviation . I believe σ = 20 in your case. Click
"OK" and JMP gives you the hypothesis test at the bottom of the
printout. Note that you cannot enter the level of significance they
have given. Note that:
JMP gives you the P-values, and you make your decision from
that. As they say, you will write out the hypotheses, list the test statistic as given by JMP, list the P-value as given by JMP, and then write your conclusion.
Prob > |z| is the P-value for a two-tailed test.
Prob > z is the P-value for an upper-tailed test.
Prob < z is the P-value for a lower-tailed test
To make the confidence interval. Click the red
triangle next to "Wait Time" 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 = 20 in your case. Click "OK" and JMP gives you the
Confidence Interval at the bottom of the printout. You can now select, copy and print your output to a file ready for upload as usual.
Yet another confidence interval and a hypothesis test to do, first by hand and then again with JMP.
To use JMP, click "New Data Table", then enter the data into Column 1. Double-click Column 1 and name it something appropriate, like "Battery Life". Now select "Analyze",
"Distribution" and highlight "Battery Life" and click "Y, Columns", then click
OK. You are now looking at a histogram and stuff.
To test the hypothesis. Click the red
triangle next to "Battery Life" then 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. Note that:
Prob > |z| is the P-value for a two-tailed test.
Prob > z is the P-value for an upper-tailed test.
Prob < z is the P-value for a lower-tailed test
To make the confidence interval. Although they didn't actually ask you to do the confidence interval with JMP, here is how you can if you want to use it as a check. Click the red
triangle next to "Battery Life" then select "Confidence Interval" from the
drop-down list. Select "Other" to get a pop-up menu. Be
sure to type in 0.97. 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 = 25 in your case. Click "OK" and JMP gives you the
Confidence Interval at the bottom of the printout. You can now select, copy and print your output to a file ready for upload as usual.
Again, take note of my question 13 in Lesson 9 when deciding if you can use the confidence interval to test the hypothesis.
http://grantstutoring.com/Study Lesson 3: Designing Samples and Experiments in the current edition of my book, if you have it, to prepare for this assignment. Note that, in older editions of my study book, this was Lesson 4.
You will need Table B to help answer some of the questions on this assignment. That is in the textbook or can be downloaded from the resources section of Stats Portal. Here is a link where you can download the table immediately, if you prefer:
Thankfully, there is no JMP needed for this stuff.
Question 1. Be sure to read my section teaching the different types of experimental design (after question 6 in Lesson 3 of my book) for some ideas on how to answer this question.
Question 4 can be frustrating because you don't know whether you are to describe what is definitely being done in your example, or what you also assume should be done. I recommend you first select the options you are certain have been done, and, if they mark you wrong, add other options that you think might have been done, and cross your fingers. Remember the three principles of experimental design while you answer this question: randomization, replication (or repetition), and control of outside factors. Note, if an experimenter does the same treatment at least twice, that is replication.
Question 5
They want two diagrams in this problem. A table that shows how you are determining the treatments (like my question 7(b) in Lesson 3) and then an arrow chart of the experiment.
Here is a link where you can download my Word document teaching my question 7(b). Perhaps you will find this helpful in making the charts your question requires:
To draw one of those arrow charts and upload it, there are many
ways to do it and it depends on how fancy you want to get and what
program you are using. A pretty simple way might be to insert a table
into your document (In Word, select Insert, and choose Table) and give
yourself lots of rows and columns to work with (I'd say at least 4
columns and 5 rows; you can always add extra rows if you need them by
just pressing the Tab button when your curser is in the last cell of the
last row). You could also use a spread sheet program like Excel.
Type in the various words you want in the approximate
positions throughout the table. To connect words together with arrows
insert arrows (in Word or Excel, select Insert, Shape, and select the Arrow).
You then use your mouse to click where you want the arrow to start and
where you want it to stop. Get rid of the lines on your table by
right-clicking your mouse while pointing anywhere in the table and
selecting Table Properties. Then, select Borders and Shading and select
None. Don't get rid of the lines until you have made your whole chart
since the lines will help you place your words throughout.
By the way, I show you how to make a table in
question 7 to identify the treatments needed for a two-factor
experiment. When you have a three-factor experiment, make a table for
just two of the factors first, then, give all of those treatments to the
first level of the third factor. You then give those exact same
treatments to the second level of the third factor, and so, until you
have used all the levels of the third factor. Make sure you number the treatments in each cell of your table, and if you have to make two or more table, use different treatment numbers for each cell.