Stat 1000: Assignment 6 Tips (Classroom Lecture Sections)
Published: Wed, 04/03/13
My tips for Assignment 6 are coming below, but first a couple of announcements.
Please note that my final two-day review seminar for
Stat 1000 will be on Saturday, Mar. 30 and Sunday, Apr. 7 (eight days later), in room 100 St. Paul's College,
from 9 am to 6 pm each day. This seminar will cover the lessons in Volume 3 of my book. I expect to also have time on Day Two to go through a Sample Final Exam.
Did you miss Day One of the seminar? I have a special offer on my audio podcasts for students who attend at least one of Day One or Day Two of the seminar. Of course the audio is available to purchase even if you do not attend the seminar at all. Click here for more info:
Did you read my Tips on How to Do Well in this Course?
Make sure you do: Tips on How to Do Well in Stat 1000
Did you read my Tips on what kind of calculator you should get?
Did you miss my Tips for Assignment 5?
Tips for Assignment 6 (Classroom Lecture Sections A01, A02, A03, etc.)
Don't have my book? You can download a free sample containing Lesson 1 at my website here:
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).
You will be using Table A and Table D while learning Lesson 8 through 11
and doing this assignment. 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.
Question 1: 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.
Question 2: Very similar to question 1. Of
course, you can use the Stat Mode in your calculator to compute the mean
and standard deviation of the given sample. For part (a),
be sure to read my discussion about the robustness of the inference for
the mean and the conditions necessary to be able to trust our
inferences just before I do question 1 in Lesson 8. Look at my question
1(b)
in Lesson 8 for an example of how to interpret a confidence interval
for
the mean in order to help answer part (c). Look at my discussion in the P-value section of Lesson 9 and my question 6 for examples of how to interpret a P-value for part (e). Be sure to look at question 13(d) in Lesson 9 to help with part f of the problem.
To use JMP for question 2:
First, open a New Data Table, name your column "Mileage" and enter the data down that column.
Select "Analyze, Distribution" and make "Mileage" 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 from your null hypothesis (make sure you read part (d) of the problem to properly understand what the null and alternative hypotheses are). 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.
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 Click "File" in the JMP toolbar and select "Save As" and save the
printout as a PDF file ready to upload into your HTML editor box.
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. Obviously, do this after you have saved your PDF file
since they don't want the confidence interval with JMP.
Click the red triangle next to Mileage above your histogram and select "Confidence Interval". Select
"Other" to get a pop-up menu.
It probably already has 0.95 typed in (for 95% confidence interval),
but you want a 90% confidence interval, so be sure to type in 0.90.
Click "OK" and you will then get the confidence interval added to your
printout.
Question 3:
First, note that parts (a) through (d) of this
problem are strictly interested in the "Social Media" data, so that is
just standard hypothesis for the mean stuff from Lesson 9 of my book.
The rest of the problem, parts (e) through (h), is
comparing "Social Media" to "Study Time". You must ask yourself, is
this a Two-Sample problem or a Matched Pairs problem? Did they select
one group of students and record their social media scores, and then
select another independent group of students and record their
study time scores? That would be a two-sample problem. Or, did they
record a social media score and a study time score for each
student? That would be a Matched Pairs problem. Of course, they do
make it kind of obvious since they entitle the hyperlink for this
question "One-Sample and Matched Pairs t."
Be sure to study Lesson 10 in my new book before
you proceed to do this and the next few questions. Those of you with an
older edition of my book will see that I teach Matched Pairs at the end
of Lesson 9, but you will lack any discussion of Two-Sample methods.
Question 4: Is yet another matched pairs problem.
Be sure to look at questions 1 and 2 in my Lesson 10 for examples.
Those of you with older books will find questions 19 and 20 in Lesson 9
are matched pairs problems.
Question 5: Is a standard confidence interval and hypothesis test
for the proportion using the formulas I introduce in Lesson 11 (or Lesson 10 if you have an older book). Note that
all the required formulas are provided on your exam formula sheet (except you
must memorize that p-hat, the sample proportion, is x/n).
Question 6 is more practise at hypotheses for proportions. Note the word "majority" as discussed in question 3 of my Lesson 11.
Question 7 introduces the sample size formula for
proportions (given on you formula sheet on the exam) as illustrated in
questions 5 and 6 in my Lesson 11. Be sure to remind yourself of the
Inverse-Square Relationship about sample size which I introduced in
Lesson 8, question 8. For part (e), compute n for p* =
0.1, 0.25, 0.5, 075, and 0.9 and see what happens to your answer. There is a
reason why we use 0.5 when p is unknown.