Stat 2000: REVISED Tips for Distance Assignment 1 (classroom sections should take a look, too)

Published: Sat, 02/04/17

I didn't realize the level of significance given in #2 caused some confusion, so I have added some extra explanation below.
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Did you read my tips on how to study and learn this course?  If not, here is a link to those important suggestions:
Tips for Assignment 1
Here is a link to the actual assignment, in case you don't have it:
Please note that I made major changes to my book in September 2014.  If you are using a book older than September 2014, you are missing about 100 pages of new material and an entirely new lesson on Probability.

Study Lessons 1, 2 and 3 in my Basic Stats 2 book (if you have it) to learn the concepts involved in Assignment 1. 

Of course, always seek out assistance from my book, your course notes, etc. if you ever hit a question you don't understand, but try not to be learning things as you do an assignment.  Learn first, then put your learning to the test.
Question 1
Be sure to study all of Lesson 1 to get a proper understanding not just for this question, but this entire assignment.  Especially look at my Lesson 1, #6, 7 and 8.  Specifically, the Inverse-Square Relationship I introduce in #8 is what they are playing with here.

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).


If it is not obvious, you can always take the two given margins of error and divide them to identify the key factor.  Always do bigger divide by smaller to get the factor.  But, be careful. 

  • Did the margin of error get biggern (is the new margin of error bigger than the old one)? Then the sample size must get smaller by the square of the factor. 
  • Did the margin of error get smaller (is the new margin of error smaller than the old one)? Then the sample size must get smaller by the square of the factor.
Questions 2 and 3
Be sure to study all of Lesson 2 to get a proper understanding not just for this question, but this entire assignment.  Especially look at my Lesson 1, #1 to #4, at least to prepare for this question. 

Question 2
Be sure to state the null and alternative hypotheses in this question.  The rejection rule they want is like what I am doing in Lesson 2, #2. 

However, you should discover that you are unable to get the z* critical value off of the t table like you would usually do.  That means you will need to work backwards from the z table instead (similar to what you would do for an unusual level of confidence as I illustrate in Lesson 1, #10). 
  1. As always, make sure you are clear whether this is an upper-tailed, lower-tailed or two-tailed test, and then shade the tail or tails appropriately for the given level of significance, α, and label the boundary on the horizontal axis z* (in a two-tailed test, you would label both a z* and a -z*, in a one-tailed test, you label strictly z*).
  2. Use that information to determine the area to the left of z*.  Never forget!  The z table deals strictly in areas to the left of z.
  3. Find the closest left area you can on the z table, and cross-reference to see what the z-score must be.  That z-score is your z* critical value.
Question 3
Use the appropriate test statistic formula and make your decision.  Similar to the approach I use in my Lesson 2, #4.
Questions 4 to 8
Be sure to study all of Lesson 3 in my book to properly prepare for these questions.

Question 4
They want what I call the x-bar decision rule here.  See my Lesson 3, #3 starting on page 131 of my book.  (Note that this entire lesson is included in my Free Samples above).

Question 5
Use the x-bar decision rule you found in question 4 above to construct an alpha/beta table and proceed to compute the power as requested.  See my Lesson 3, #4 and #5, especially for examples.

Question 6
Remember the alpha/beta/power chain I discuss in the early part of Lesson 3.

Question 7
Remember the n/beta/power chain I discuss in the early part of Lesson 3.

Question 8
Read my important discussion in Lesson 3, page 148 about the relationship between the alternative mean and the power of a test.
Questions 9 to 13
Now you are back to Lessons 1 and 2 of my book, but this time we are using t. (Why?)  Be sure to use the values they gave you for the sample mean and sample standard deviation (don't use your Stat mode to compute the values yourself, since your answers may have too many decimal places).

Question 9
Just a good old confidence interval, similar to my Lesson 1, #2.

Question 10
Standard hypothesis test stuff.  Be sure to use the information given prior to question 10 to state the null and alternative hypotheses.  Now, they want you to compute the test statistic.

Question 11
Be sure to look at the P-value section of my Lesson 2, starting on page 80.  Especially look at my examples 8, 9, and 10 starting on page 85 to understand how to put bounds on a P-value when using t.

Question 12
Obviously, use your P-value to make your decision.

Question 13
Now they want the t decision rule, by first getting the appropriate t* critical value, similar to my t examples in Lesson 2, #2.